The Red Devils are facing off against Liverpool at Old Trafford in the Premier League.
It is a key game for United and Solskjaer, with the latter in danger of losing his job if the team suffers a humiliating defeat.
And he spoke about how Martial and Wan-Bissaka could play some part in the game after recovering from their respective injuries.
Solskjaer told Sky Sports: "I can't tell you 100 per cent [who] is going to be fit as something might happen.
"But hopefully Aaron and Anthony will last through the training this week and be available for selection.
"If it's for half a game or 30 minutes, I don't know, but let's see where they're at."