Solskjaer is now the favourite with the bookies to become the next permanent manager of Manchester United.
The former striker has won eight of his nine games since taking interim charge in December.
However, Ince would rather see Tottenham boss Mauricio Pochettino given the job.
Chris Sutton asked Ince on BT Sport Score: “If he [Solskjaer] gets into the top four, should he get the job?”
Ince replied: “No I don’t believe he should. I think he’s up there, I think he’s got to be on Edward Woodward’s mind.
“But I also think someone like Pochettino will be also.
“We’ve spent three to four years, maybe longer, with [Louis] Van Gaal, [Jose] Mourinho, just wasting time.
“The next man we get in has to be the right man. People will say it’s hard to say who’s the right man until he actually gets in there.
“People say to me ‘why would you want Pochettino? He’s not won anything’.
“That’s a poor, poor remark that he’s not won anything. Ole Gunnar Solskjaer’s not won anything.
“We know as players it’s about winning trophies, United’s been built on winning trophies.
“But when I saw Tottenham play the second half at Wembley against Manchester United, looking at the way Tottenham were playing, I was thinking I’d love to see a Man United team play like that week in, week out.
“I would love to see Pochettino, I really would.
“Ole’s done a fantastic job and I think it’s easy for fans to start clambering for Ole.
“Things can go wrong, hopefully they don’t at Man United.
“Everything’s going hunky dory, they’re winning games.”