The source, whose name was not reported, said the couple are getting more serious about their relationship.
"John has given her the confidence to jump out of the rat race. With John, she feels like herself. She wants to nest. She's gained a few pounds, is taking a much-needed break from work and perhaps is even getting her mind and body ready for pregnancy," the source said.
Actor Russell Brand, Perry's ex-husband, had previously hinted that the reason the two divorced is because she was too career-oriented and didn't want children, Entertainmentwise reported Friday.
"She's young, successful and dedicated," Brand said in an interview with Howard Stern. "[The reality is] you can't fully understand it until you do it. I was really into the idea of marriage and having children."
Mayer has a reputation for dating and dumping some of Hollywood's hottest stars, Entertainmentwise said.
"John really likes the fact that Katy is so independent and not needy and clingy like the other girls he's dated.
This is the first time John's felt so strongly about a girl. She's played her cards perfectly," the source told More magazine. ''They really do bring out the best in each other. It wouldn't surprise me at all if he proposed.''
Celebrity Couples of 2014 [PHOTOS]