The interim United boss has made a perfect start in the Old Trafford hotseat, winning all eight of his games in charge, but is still set to return to Molde at the end of the season as it stands.
Solskjaer enhanced his reputation with big wins at Tottenham and at Arsenal on Friday, leading to growing calls for United to offer the Norwegian the vacancy long-term.
However, Ince, who won two league titles during six years at Old Trafford, has urged his old side to hire the right man instead of someone with just strong links with the club.
The 51-year-old does not want them to go down the same road as Chelsea when they replaced Andre Villas-Boas with ex-Blues star Di Matteo.
The Italian came in and steered Chelsea to the FA Cup and Champions League in 2012, appointed on a two-year deal, but was then sacked five months later.
Ince told Match of the Day: “Solskjaer has come in and lifted the cloud over Manchester.
“The players are playing with a lot of freedom. The shackles have been released.
“They’re playing entertaining, attacking, progressive football which the fans have been crying out for for quite a while.
“It’s a big job, Manchester United. It’s not about now, it’s about the future. To bridge the gap between Man City and Liverpool is a massive job.
“All Ole can do is keep on winning, hopefully win a trophy, get into the Champions League spots — or win the Champions League — then he’s asking questions of Ed Woodward.
“I think it’s easy to give him a season. Chelsea did that with Di Matteo.
“He came in, won the Champions League, won the FA Cup, lasted three or four months.
“The next man for Manchester United has to be the right person, so they’ve got to make a decision at the end of the season.”
While Solskjaer’s case gathers more momentum with every win, Tottenham manager Mauricio Pochettino remains United’s No1 target.
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