The 35-year-old is said to have scheduled meetings with estate agents so that he and Perry can get their own place together, reported People magazine.
"He always insisted he needed his own place to make music but clearly that's changed. Now he mostly hangs out at Katy's place in Los Angeles," a source said.
While the couple was initially reluctant to go public with their relationship, they are now serious and feel confident about their future together.
"They have both acted very private about their relationship in the past, but they seem comfortable about going public with their relationship now. They seem very happy," the source added.
It is even rumoured that Mayer will propose to Perry soon.
"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. They really do bring out the best in each other. It wouldn't surprise me at all if he proposed," the source said.
Perry was earlier married to Russell Brand.