Let's take a look back at 44-year-old Cooper and 33-year-old Gaga's close bond.
Gaga says the biggest reward of filming A Star Is Born is her "lifetime friendship" with Cooper:
Last November, ET spoke to Gaga when she supported Cooper as he was awarded the 32nd American Cinematheque Award, and she gushed about his talents.
"He is such an incredible director and, you know, he made me a better actress," she said. "I just love him so much and he is such a dear friend of mine and I am just so proud to be here tonight."
Gaga explained that the two had remained friends even after production on the film wrapped.
"We talk all the time, yeah," she shared. "And it's exciting and wonderful and we are both so grateful for how the film is being received. You know, that's what's really come out of all of this for me: the reward of a lifetime friendship with someone I deeply respect."
Gaga and Cooper give an intense performance of "Shallow" at the Oscars:
"I was like, 'Are they doing it?' It was so good," Haddish told ET at the Vanity Fair Oscars Party red carpet.
More Twitter comments included, "If you try to tell me Bradley Cooper and Lady Gaga aren't in love, I am going to call you a liar," and "Bradley Cooper and Lady Gaga acting like they’re the only people in the room for 3 minutes straight."
Gaga left no room for speculation on anything romantic happening between her and Cooper when she spoke to Jimmy Kimmel after the performance.
"First of all, social media, quite frankly, is the toilet of the internet and what it's done to pop culture is abysmal," Gaga said, rolling her eyes at the rumors. "People saw love and, guess what, that's what we wanted you to see. This is a love song. The movie, A Star Is Born, it's a love story."
"From a performance perspective, it was so important to both of us that we were connected the entire time," Gaga added of the intimate nature of the Oscars performance. "When you're singing love songs, that's how you want people to feel."
Gaga and Cooper have "endless chemistry," a source tells ET:
In February, a source told ET that the close co-stars had kept it professional from the start when working on A Star Is Born together and had incredible chemistry.
"They are both very hard-working, driven people and during the making of the film, had a very professional work relationship," the source said. "From the moment they began collaborating with each other, people on the set saw how connected they were, which is why everyone wants their relationship to be real. There is endless chemistry between them.”
"When they're together, they complete each other sentences," the source continued. "They are creatively so in tune with one another and seem to have a total intuition with one another."
The source noted at the time that Cooper was still very much with Shayk, and in fact, the model was snapped hugging Gaga during the Oscars ceremony.
"The Oscars fueled their love story even more," the source said of Cooper and Gaga's interaction at the Academy Awards. "But what really happened behind the scenes of the Oscars was a sweet conversation between the two of them. Lady Gaga thanked Bradley for making her dream of becoming a movie star come true, and Bradley thanked Gaga for making him a rock star."
Cooper's ex-wife comments on all the romance rumors:
Still, rumors continued to swirl around their performance, prompting even Cooper's ex-wife, Jennifer Esposito, to comment.
When David Spade Instagrammed a photo of the performance and wrote, "Is there any chance these two aren't f**king?," Esposito cracked, "Ha."
"I literally laughed at [Spade] because he was so bold in what he was saying and I thought it was funny," Esposito explained on Instagram. "I'm allowed to think something is funny."
"I didn't watch the Oscars, I don't know what went on, I don't care what went on," she continued. "I just commented on something that I thought was funny. ... To find that people are making judgement calls about me, or them ... is really psychotic."
A source tells ET that all the romance speculation definitely didn't help Cooper and Shayk's relationship:
Earlier this month, a source told ET that Cooper and Shayk have actually been dealing with serious relationship issues even before he started filming A Star Is Born. Still, according to the source, the romance rumors surrounding him and Gaga wasn't ideal.
"Things were difficult before Bradley started filming A Star Is Born but his dedication to his work while making the movie only made things harder at home," the source said. "The constant speculation about Bradley's relationship with Gaga -- while things were difficult at home -- didn't help the situation. But his relationship with Gaga is not the issue. They have many daily issues as parents and as professionals and have been fighting."
"Their troubles have been going on for quite some time and they even considered splitting during the release of the movie," the source continued. "They talked things through a great deal and seemed to hold off and keep up appearances for the time being. It was recommended they delay a split at what seemed to be the peak of his career because the negative attention would take away from the excitement of the release."
A source tells ET that Cooper and Gaga being so focused on their work affected their personal relationships:
"Christian and Irina have a lot in common, they both feel they lost love because of their partners' endless work and dedication to their careers," the source said. "Christian liking Irina's Instagram photo is just his way of being supportive of her."
The source added that Cooper and Shayk grew apart due to the actor being more focused on supporting A Star Is Born, while she was more involved with their 2-year-old daughter, Lea De Seine.
"After the movie was complete, Bradley became very involved in the promotion of the film, while Irina became very involved with the baby," the source said. "They argued a great deal, and it affected their home life. Their relationship didn't work out because Irina was looking for more of a family life."
Some fans still want Gaga and Cooper to date:
Some fans are still hoping for Gaga and Cooper to be in a romantic relationship now that they're both single.
"Quite frankly, I think the press is very silly," she said of the romance speculation. "I mean, we made a love story. For me, as a performer and as an actress, of course we wanted people to believe that we were in love."
"We wanted people to feel that love at the Oscars," she added of their much-talked-about performance. "We wanted it to go right through the lens of that camera and to every television that it was being watched on. And we worked hard on it, we worked for days. We mapped the whole thing out -- it was orchestrated as a performance. In truth, when we talked about it, we went, 'Well, I guess we did a good job!'"
Winfrey noted that she had her own conversation with Cooper about the performance.
"We were talking about all the rumors about you guys last year," Winfrey told Gaga. "He said if they had been true, he never would have been able to look you in the eye sitting at that piano. He said his Catholic guilt would have never let him be able to look you in the eye at that piano."
Gaga agreed and replied, "Absolutely."
To see Gaga talk about the romance rumors, watch the video below: