The Red Devils have enjoyed a welcome return to form under an interim boss, goal.com reported.
Since succeeding Jose Mourinho in December, a treble-winning hero of United’s past has overseen a 10-game unbeaten run – with nine victories collected along the way.
Solskjaer is now firmly in the frame to be handed the reins beyond the end of the season, but Ince feels a “proven” option should be sought in order to avoid the coaching issues which have blighted the Red Devils since Sir Alex Ferguson headed into retirement.
“United cannot afford to appoint another manager and sack him again after two years, or less,” Ince told BBC Sport.
“Compared to their rivals, they have gone backwards in the past few years while City, Liverpool and Spurs have all built and progressed.
“They are going in the right direction now, but there is still a lot of work to do for them to get close to those teams again.
“So, who should get the United job in the summer? My choice would be Mauricio Pochettino because he has got a proven track record as a Premier League manager over several seasons. Solskjaer doesn't.
“And, everything United need from their next manager, we know Pochettino can do – based on what we have seen from him at Tottenham.
“He can build a team that can challenge for the title, playing the right style of football too. We saw what Spurs did to United at Wembley last month – yes, United won because of the brilliance of David de Gea in goal, but that is how I want to see a United team play.
“And, while I am not saying Solskjaer definitely shouldn't get the job, I just think he would be a gamble, while Pochettino has the kind of CV you would want from a man who should be United manager for the next four or five years.
“That is the way United should be thinking now. They have got their last three appointments wrong, so they need to get the next one right.”
Ince added on the need for United to wait until the end of the season before making a call on Solskjaer, “I think it is great that the United fans are desperate for Solskjaer to get the job but let's not be too hasty about giving it to him now.
“If United finish in the top four and they win the Champions League or reach the final in Madrid, then his name is going to be very high on executive vice-chairman Ed Woodward's shortlist in the summer.
“But the next month is massive for United, and I do not mean for Solskjaer's job prospects – I am talking about their hopes of winning a trophy this season. That is what the focus should be on now, and he has alluded to that himself.
“Solskjaer has already said that silverware is his target, and the exciting thing for me is that they have got a real chance in the FA Cup, and in Europe.
“Mourinho was still United's manager when the draw for the last 16 of the Champions League was made, and if you had asked me then about whether they would get past Paris Saint-Germain, I would have said they are out of it.
“Now, because of the way they are playing, I am starting to believe in them again.”