The Wales manager, 45, is enthusiastic about the prospect of his former team-mate ruling the roost at Old Trafford.
He told the Guardian he thinks the club have dithered for too many years now, leaving United behind their major rivals.
Asked if he thinks Solskjaer should get the role, Giggs said: "I do.
"We’ve messed around far too long.
"When you’ve got someone who knows the club, who is tactically astute, clearly has the players and fans on board, that gives you lots of momentum.
"There will be bumps in the road but most fans imagine what he could do with the money that’s been spent the last few years."
Mauricio Pochettino is also a front-runner on Ed Woodward's candidate list to take over the job full-time.
But Giggs — who is not in the running for the job this time — has urged the club to come up with a blueprint to become the best in the world again.
He added: "Planning is more important than the announcement.
"Look at Guardiola. He got in Man City players he wanted the year before he took over.
"So, if it is Ole, keep it amongst the club and start planning. Our problem the past few years is that we were always playing catch-up.
"We should identify the two or three players we need if we’re going to win the Premier League and Champions League."
Giggs also revealed that he was never offered the Old Trafford job by the United board, despite being constantly tipped as the next United boss by Louis van Gaal, before the club appointed Jose Mourinho.
He was Van Gaal's assistant for two seasons, before the Dutchman was sacked in 2016.
Giggs said: "It was more Louis [van Gaal] who said it. You know how Louis is. He told Ed Woodward [United’s executive vice-chairman]: ‘I will be manager for three years and then Ryan will take over.’"
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