Solskjaer found himself under pressure after a disappointing start to the season, but his side produced some of their best football of the season to see off Spurs, and now head into the Manchester derby full of confidence.
And several senior figures within the United dressing room told Ed Woodward and the board to keep faith with boss Solskjaer, reports The Times.
The plea was reportedly made before the victory over Spurs, which saw United climb to sixth in the Premier League.
United's players have remained behind Solskjaer throughout their tough start to the season.
And speaking after the Old Trafford victory, Solskjaer said: "I feel no fear whatsoever here. I feel at home, I enjoy myself and I'm going to enjoy myself for as long as I can.
"We've just got to go and get as many points on the board as possible. I said before this game that it's a great chance for us to show what we can do."