The Norwegian has been sweating over the fitness of five players ahead of the Old Trafford clash, with Pogba (ankle/foot), Martial (thigh), Jesse Lingard (illness), Luke Shaw (thigh) and Aaron Wan-Bissaka (back) all struggling during the international break.
Lingard and Wan-Bissaka were forced to withdraw from Gareth Southgates squad for Englands Euro 2020 qualifiers against Bulgaria and Kosovo, but there is a chance the pair could feature this weekend.
While Pogba and Martial have both been ruled out of the game, Solskjaer is hopeful the French duo can return in time for the sides trip to West Ham on September 22.
United left-back Shaw will also be unavailable on Saturday as he steps up his recovery from a thigh injury.
Asked about Pogbas fitness, Solskjaer replied: Pogba wont be fit, no, unless hes had a miraculous recovery overnight from yesterday to today or tonight to tomorrow.
Hes not been ready to do 100 per cent training, no.
We hope more can be ready for West Ham next week and Paul and Anthony are in that category, I think theyll be ready for then and cant say more than that really.
Solskjaer believes there is a chance Wan-Bissaka and Lingard could feature versus Brendan Rodgers side on Saturday.
The treatment rooms been busy and it still is, Solskjaer added.
So we dont really know whos going to be available.