The Norwegian is being considered for the position full time after a stunning first two months in the job.
And in attendance at Craven Cottage was executive vice-chairman Ed Woodward, as well as co-chairman Avram Glazer.
It was the first match Glazer has been at since United’s defeat to Juventus at Old Trafford in October.
Meanwhile, Solskjaer’s representative Jim Solbakken was also in the directors’ box at Fulham.
And according to the Manchester Evening News, he spoke with the United board members.
Solskjaer revealed after the game how he met Glazer in the dressing room after as they celebrated the latest triumph.
The manager, though, kept what they discussed close to his chest.
“The Red Devils have maintained no final decision will be made until the summer”
But the attendance of Solbakken and Glazer at the game in particular is considered potentially significant, given United are still weighing up who will be their next permanent manager.
Solskjaer has put himself firmly in contention, with Tottenham’s Mauricio Pochettino still a top candidate too.
The Red Devils have maintained no final decision will be made until the summer, when Solskjaer is due to return to Molde.
However, the fact Glazer, Solbakken and Woodward met though, and so publicly, at Fulham does suggest there is a distinct possibility discussions are being held over Solskjaer’s future.
Club chief Woodward, who is leading the hunt for Jose Mourinho’s full-time successor, usually attends every United game.
And the Manchester Evening News adds he is often visiting the dressing room after the matches to congratulate players.
The Glazer siblings are also said to have entered the dressing room in the past.
Everyone at Old Trafford will be hoping there will be more reason to celebrate come Tuesday too when United take on injury-plagued PSG in their Champions League round of 16 first leg.