Current Molde coach Solskjaer has been one of a number of managers to be linked with the job when Sir Alex Ferguson decides to end his tenure at Old Trafford.
However, despite having previously admitted that he would like to take on the role, Solskjaer believes that it is a responsibility that veteran midfielder Giggs could handle.
"Giggsy is going to play another year but I'd say he's got his eyes and ears open more to what the manager is doing," Solskjaer told reporters.
"He's looking at that United job for himself, Giggsy. He's got top potential."
Giggs is known to have taken some his coaching badges in preparation for when he retires from playing.