Ole, who is enjoying a successful manager reign at Molde, has himself been linked with the job.
“He’s looking at that United job for himself, Giggsy. He’s got top potential,” said Solskjaer.
“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.”
On the other hand, Sir Alex Ferguson shows no signs of giving up the job, but Ole believes that he has noticed some signs that has made him think that Giggs might be the next Manchester United boss.
Solskjaer was also linked to other BPL clubs like Aston Villa and Blackburn, but the Norwegian wants to stay in his home country and gain experience.
Although he admits that managing his former club might be like a dream come true, yet he believes Giggs is a natural contender for the job.
“You have to dream big – if you don’t dream big, you won’t make it. So let’s just wait and see what happens,” he added with a smile.
“Giggsy will know that. He’s got real potential and he will be looking at what the manager is doing.