"We should find a spot for him to be on the show," Morrison, 32, tells PEOPLE. "That would be awesome. He's a living legend. He just brings such a great energy and a great validity to everything he does."
What sort of role does the actor, who plays Mr. Schuester, see for John?
"He should do something with Jane Lynch," Morrison says, referring to the Golden Globe-winning actress who plays Glee's no-nonsense cheerleading coach, Sue Sylvester. "I think he should maybe play her boyfriend or some kind of love interest for her. I think that would be funny."
Working on his album with new dad John, 63, was what Morrison calls "an out-of-body experience." "I didn't really believe it was actually happening," says the actor. "I actually felt like I was a bad singer because we were singing a couple of his songs, and you're so used to hearing that voice on these songs, and I'm like, 'I don't sound good on these songs.' "
Despite any insecurities on Morrison's part, the musicians' collaborations were hailed a success by John, who has already talked up the duo's time in the studio.
"It was supposed to be a secret that he was going to be on my album, but he's kind of telling everyone," Morrison says with a laugh. "So I guess we can talk about it. He's just the most loving man, and we had the best time. He was so giving and so supportive. We just had a ball."
Fans eager to hear the singers' duets will have to wait until next month's release of Morrison's album. Until then, he plans to play a free show on Jan. 29 – his first live performance in his solo career – at The Grove in L.A., as part of Oscar Mayer's Good Mood Mission.