"Jennifer and Alex are madly in love," the source revealed. "They are the real thing."
The pair made their official red carpet debut as a couple on Monday at fashion's biggest night, the Met Gala in New York City. Lopez, 47, wore a stunning powder blue Valentino gown, while Rodriguez, 41, complemented her look in a black-and-navy tuxedo with Harry Winston Premier Diamond Cufflinks.
"Everyone who saw them on Monday night could see how super into each other they are. They didn't leave each other's side for a minute," the source continued. "Wherever Jennifer went, Alex followed. They only had eyes for each other."
But don't expect Lopez and the former MLB pro to be walking down the aisle anytime soon -- the source also told us they "don't think marriage is on Jennifer's radar at the moment."
"She's been married three times already," the source noted, referring to her previous nuptials to Ojani Noa, Chris Judd and Marc Anthony. "She has two beautiful kids who are the focus of her life. I think she’s at a point in her life where she doesn't need a husband to feel like she's in a committed, loving relationship."
"Alex is a gentleman and fortunately has a lot of free time right now to be the perfect boyfriend," the source added. "He focuses all his energy and time into Jennifer, who always has a million things going on. They balance each other well and have a great time together. I don't think she needs another engagement ring or a marriage certificate to be happy."
Lopez and Rodriquez are both parents, and recently introduced their children to each other. The singer shares two kids, 9-year-old twins Emme and Maximilian, with Anthony, while Rodriguez shares two daughters, 12-year-old Natasha and 9-year-old Ella, with ex-wife Cynthia Scurtis.
Hear more on how J-Rod's love story has evolved in the video below!