"He's put himself as a front runner (for the permanent role at United) for sure, he has done incredibly well," Schmeichel was quoted as saying by Sky Sports.
"It's been really good to have this Manchester United mentality, culture, identity back at the club. You only have to look at the results to see how important that has been."
United have earned 29 points in the league since the Norwegian was appointed, more than any other team in that period.
"You can argue it's a free ride for him because he's there on a short-term basis and he's going to be evaluated for the job on a permanent basis," added Schmeichel, who played alongside Solskjaer in the United team who won the Champions League, Premier League and FA Cup in 1999.
"But you know he can go on and he can set his team free, go and attack, go and have fun, commit people forward and try to score goals."
Fifth-placed United host Southampton on Saturday.
(Reporting by Rohith Nair in Bengaluru, editing by Ed Osmond)
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