From an interview with Red (link below):
Elvis didn't listen much to his own music but he really loved his From Elvis In Memphis album, the one he did with Chips Moman; that was an album full of great songs and Suspicious Minds by my buddy Mark James. Elvis was so sick of this movie crap that he'd been recording and it was not doing his career any good. When he cut that album it (The session) was just loaded hits, In The Ghetto, Suspicious Minds, Don't Cry Daddy, Kentucky Rain. He brought the demos when he was doing the Change of Habit film with Mary Tyler Moore. He wore Suspicious Minds out. When his albums were released he would listen to them and think about them and wonder if he had done this or that or the other. But the one he played more than any was that Memphis album.