The former Red Devils striker is currently impressing in his first managerial role at Molde and has guided the club to back-to-back Norwegian Premier League titles.
Solskjaer has been touted as a possible candidate to replace the 71-year-old United manager when Ferguson finally decides to end a decorated career.
But the Norwegian reckons Red Devils midfielder Giggs, 39, who recently signed a one-year contract extension, is eyeing his boss’s job.
“He’s looking at that United job for himself, Giggsy. He’s got top potential,” Solskjaer told the Daily Mirror.
“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.
“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: “Giggsy will know that. He’s got real potential and he will be looking at what the manager is doing.”
On his own ambitions to succeed Ferguson, Solskjaer admitted that he would love to become United manager in the future.
“I’ve said it before that my dream is to manage Man United,” he added.
“That’s tongue in cheek, really, because it’s a massive job – the biggest job in the world.”
Solskjaer scored 126 goals in 366 appearances for the Red Devils in 11 seasons at Old Trafford after joining from Molde in 1996.