Solskjaer said last week the owners of Norwegian club Molde, who sent him to Old Trafford with their blessing, had asked him to try to turn his temporary stint into a permanent role.
Solskjaer's side face Fulham in the league on Saturday.
It was a remarkable turnaround for a club that won three-of-the-first-four MLS Cups after the league launched in 1996 but had fallen on tough times in recent years.
Paul Pogba is the most obvious case, the France midfielder struggling badly under Mourinho but quickly showing his class in United's revival.
"It's just different random things, just to make you think and it's to kind of push each other because you want your friend to be successful as well". 10 games; nine wins, one draw, and zero defeats, while he has taken 22 points from a possible 24 in the Premier League.
New Zealand beats India by 80 runs in 1st T20
The wicket-keeper batsman blasted a 43-ball 84 to lay the foundation of New Zealand's 219/6 against India at the Westpac Stadium. Ms Dhoni scored 39 off 31 but his innings lacked the skills or the intent to get India off in a steep chase.
And Solskjaer has revealed that he's explained to Ed Woodward what his vision for United is and what the team would look like in 2020.
Former Everton striker Wayne Rooney believes he could still do a job in the Premier League, according to CNN Sport.
"But decisions, sometimes of players' futures are not down to me, either".
Solskjaer has earned acclaim for his impact on the team, moving away from the pragmatism which typified Mourinho's reign and bringing back more of an attacking style of play.
Claudio Ranieri does not think Fulham's upcoming clash with Manchester United is a foregone conclusion, pointing out the Red Devils' unbeaten run must end at some point. "We must be concentrated and strong, positive to show our personality during the game".
"When the chance came to buy him, I said, "Take this guy, because for me he could have a good future".