Solskjaer has been credited with helping United rediscover their attacking traditions, and has overseen Anthony Martial take a U-turn on his future, signing a deal until 2024, while Marcus Rashford is also in talks for a new contract.
One of Solskjaer's most significant contributions following his arrival from Molde has been putting a smile back on the faces of his players.
United can look back on a decent head-to-head record against their next opponents, having won eight and lost none of their last 10 duels with Fulham, with the Cottagers winning just three of the last 27 league encounters between the teams.
"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".
United's renaissance has sparked hopes of a memorable end to what had been turbulent season.
Ed Woodward centre has a decision to make over over the next permanent Manchester United manager
"He deserves it at the moment", Ranieri said.
"Now he has got this freedom to play with, I think we are beginning to see the real Paul Pogba play".
Victory at Craven Cottage would take United into the top four for at least 24 hours, and that is something that barely seemed possible when the Norwegian arrived with his side staring at an 11-point deficit from the Champions League qualification spots.
And this feels like a match where Solskjaer may feel he can get away with playing Juan Mata on the right - although he would be wiser to deploy him through the middle - to give Jesse Lingard the chance to rest before being unleashed in midweek. He was a fantastic player. "Why not?" said Ranieri, whose side are second bottom after one win in their past five league games.