The couple went public with their relationship in June 2020.
"They're very in love and beyond obsessed with each other," the source says. "They are ready to take this next step in their relationship."
ET has reached out to MGK and Fox's reps for comment.
The couple recently covered British GQ Style's Autumn/Winter 2021 issue, and opened up about their intense relationship, which began last year after they worked together on the film Midnight in the Switchgrass.
"It should be light, but also we go to hell with each other. It's ecstasy and agony for sure… I don't want people to think anything's perfect with us. I didn't say it was the darkest fairy tale for no reason," MGK said. "I came from broken homes and I watched love never work. Then I grew up where in pop culture they don't even make romantic movies anymore. It hurts my soul that I wasted 30 years of my life not having any desire."
"[I was] definitely open [to] love, but I did not anticipate walking right into my soulmate like that," Fox said. "I was obviously over the way I had been living, and those paths lined up, those doors opened. It was [as if] all the obstacles that had kept us apart all those years [had been removed] and we were able to finally intersect."
The engagement chatter has been swirling for a while, as a source told ET in June that MGK and Fox "are pretty inseparable."
"MGK would love to start a family with Megan someday, but right now doesn't seem to be the time in terms of scheduling," the source said. "As far as engagement goes, it is likely that this will happen sooner than later and it has been a topic of conversation without question. Their schedules are starting to get super busy again, so they just want to make sure that the timing is right since it would be a big step for both them and their families."
Watch the video below for more on the couple.