A £45million bid is expected to be made by United, with Solskjaer and executive vice chairman Ed Woodward sitting to discuss the deal this week.
Solskjaer - who was appointed until the end of the season after Mourinho's sacking in December - has overseen four successive victories.
The Norwegian has already revealed that he will be involved in talks over any January transfer targets, and The Mirror reports that he will also now help decide the futures of players soon to be out of contract.
"Hopefully he'll be OK for next weekend", Solskjaer said.
"I thought it was a professional performance away against Newcastle - and today, it's never easy when you make nine changes, but we still won all of them". 'Whatever competition you're in, you want to win.
As for the visitors, second bottom of the Sky Bet Championship, Jose Gomes' side have now gone 11 games without a win. "Even though we've got plenty of games, we need to work". "There will be tougher times coming, there will be tougher games coming up, we know that".
Against Reading, the Belgian was giving his first start and capped it without another goal just before half time, a blow to a Reading side who would have fancied their chances at 1-0 down.
From Sanchez's through-ball, the onrushing Lukaku rounded Jaakkola to score from a tight angle.
At Old Trafford the system was in use as it prepares for its introduction into the Premier League next season and VAR was called into question 20 minutes into the match.
"Through the middle, just facing the goal at all times and he knows that I am risky in that manner but also helping the team off the ball and stuff like that".
Burnley were awarded a penalty for a foul on Matej Vydra but just as he was running up to take the spot kick the referee Simon Hooper indicated that the decision to award the spot kick had been reversed because of an offside decision.
United will travel to Dubai for warm-weather training after Saturday's game, and Solskjaer warned it will not be a holiday.