The former United striker and current boss of Norwegian side Molde, Solskjaer has been linked with the United job after starting his coaching caeer with their reserve team.
Giggs, 39, who is likely to stay for another year after signing a contract extension, has previously stated that he would like to move into management in the future.
"He's looking at that United job for himself, Giggsy," Solskjaer said. "He's got top potential. 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, who made 366 appearances for United scoring 126 goals in a 15 year career at Old Trafford, was also eyeing to manage United once Ferguson hangs his boots.
"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," he said.
Solskjaer remained at Old Trafford till 2011 and managed the reserves for three years, but returned to his native in Norway to manage former club Molde. The Norwegian side won the league title in 2011, retaining the crown in 2012.
The former Old Trafford star who scored a last-minute winner against Bayern Munich in the Champions League in 1999 to help United win the treble, was also linked with a move to Aston Villa and Blackburn Rovers, but insisted he was happy to stay in his homeland and gain more experience.
"You have to win the league every year to be regarded as the best team in Norway, and we want to be regarded as the best team in Norway," Solskjaer said.
"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.