The three players have missed several games of late due to injuries.
Solskjaer is yet to make a decision on their availability.
"Hopefully, Aaron and Anthony will last the training this week and be available for selection," Ole added.
A look at how Liverpool and United have fared
Liverpool have made a perfect start to the season with 24 points from eight games.
The Reds are in red-hot form and will look to equal Manchester City's record of 18 consecutive top-flight victories when they visit Old Trafford on Sunday.
United have registered just two wins so far and are 12th.
They have won just once in their last five games.
Liverpool could hurt United at Old Trafford
Liverpool enter the high-octane clash at Old Trafford as the favorites. They are playing solid football under Jurgen Klopp and looks set to pocked another victory. If United lose, then the pressure on Solskjaer will increase drastically. The hosts are in danger of falling behind.