The West Londoners are unbeaten in eight games since Tuchel took charge and are just two points behind fourth-placed West Ham ahead of the weekend's action.
Chelsea will close to within three points of second-placed United if they win Sunday's showdown.
But the manager has his own reasons for desperately wanting a victory after Solskjaer's side famously staged an unlikely second-leg comeback to beat Tuchel's PSG team in the Champions League two seasons ago.
United became the first team in European Cup history to overcome a 2-0 first-leg deficit away from home, winning 3-1 at the Parc des Princes to progress on away goals.
Marcus Rashford's decisive injury-time penalty following a contentious handball call meant PSG were eliminated at the last-16 stage for the third season in succession – and Tuchel admitted the result left him “in a very dark place”.
“I didn’t experience anything like this ever again or before,” he said.
Tuchel said the disappointment of that defeat will continue to provide motivation for him ahead of Sunday's clash against United – admitting that he is not “a good loser”.
And he called on his players to deliver revenge on his behalf at Stamford Bridge.
This article was most recently revised and updated 2 years ago