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But, the Norwegian believes his former team-mate is the one most likely to take over from the Scot.
He told The Daily Mirror: "He's looking at that United job for himself, Giggs. He’s got top potential.
"Giggs 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 - who has been linked with Aston Villa and Blackburn in the past - admits he would love to take charge at Old Trafford but was quick to endorse Giggs as Sir Alex's immediate replacement.
"You have to dream big - if you don't dream big, you won't make it," he added. "So let's just wait and see what happens.
"Giggs will know that. He's got real potential and he will be looking at what the manager is doing.
"I've said it before that my dream is to manage Man United. That's tongue in cheek, really, because it's a massive job - the biggest job in the world."