The Cameroon goalkeeper is on-loan with Trabzonspor this season, while late summer arrival Senne Lammens is establishing himself as United's No1.
Strachan told Esports News: "I think Andre Onana has played his last game for Manchester United.
"At United you must have a presence in goal - whether it’s physical, attitude, or character, you have to be a presence. I don’t think he had that when he played for the club.
"A big problem for me is that I'm not sure Onana really wanted to be at Old Trafford. He looked like he’d rather be somewhere else and that might be what he needs to start enjoying his football again.
"At no point did I think he was enjoying playing football for United. I'd be shocked if I saw him play again for the club. I think his United career is over in that respect."