Anthony Martial's stunning solo goal and a Paul Pogba brace propelled Manchester United into the top four for the first time since the opening weekend of the season as embattled Fulham's plight worsened.
Solskjaer said he had met United owner Avram Glazer after the game, but he wouldn't be drawn on whether they would have any further meetings to discuss his future at the club.
Solskjaer made it 11 wins out of ten and continued his unbeaten run at Craven Cottage yesterday as the Red Devils breezed past Fulham 3-0 to go into the top four.
"You look at [Mauricio] Pochettino, who is the obvious choice, it looks like he wants to stay with a big project at Tottenham".
The result at Craven Cottage - a 10th win out of 11 for Solskjaer - lifted United into the top four for the first time since August.
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Paul Pogba scored a brilliant goal from an nearly impossible angle, while Anthony Martial scored an excellent solo goal to double the lead for Solskjaer's men.
"I don't really like to compare players, but I know that Paul is in good form, in a good place at the moment", Solskjaer said. The spotlight will be on United's record signing to perform against the perennial French champions but he goes into the game in the best form of his Manchester United career. "It's the players who play, it's the staff, how we do things at Carrington, at the training ground, the mood, it's never about one person when the team is winning games".
"You've got to trust the players, because the league is vital for us but it's a chance for them to say "I should play on Tuesday".
Defeat for Fulham leaves them 19th in the table, with supporters jeering manager Claudio Ranieri's substitutions and with louder boos heard at full-time.
The closest United have come to losing since Solskjaer's arrival was against Burnley at the end of January, when they came back from 2-0 down to seal a draw. "He came into the dressing room". "First, it seemed very hard for us to reach the Champions League places in the Premier League and we are already there". Of course, they're all happy after winning the game. We conceded the counter-attack, and at that point it was more hard.