The Norwegian has transformed the Red Devils’ fortunes since replacing Jose Mourinho on a caretaker basis in December, leading them to 10 victories in his first 11 games in charge.
Asked by The Guardian if he thinks that Solskjaer should be handed the job on a full-time basis, the current Wales boss 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.
“I wouldn’t be in any rush because you don’t want to derail the current situation. Planning is more important than the announcement.
“Look at [Pep] 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 denied wishing he had been the former Old Trafford great brought in to turn things around at his old club - although he admitted “it might have been different if I wasn’t the Welsh coach” - and insisted he knew from their playing days that Solskjaer had what it takes to succeed as a manager.
“Ole’s done a fantastic job,” he said. “I’ve obviously been in touch with him and he’s given players freedom and also done well tactically. The confidence is huge. He’s got smiles back on their faces.
“He’s got that steely determination because he’s been through a lot. When he was young he went to a different country. He had huge success but he wasn't always picked.
“He studied the game while he had a bad injury and then he coached at the club. So I always thought he had that potential because he knows the game and has that inner steel.”
Giggs was assistant to Louis van Gaal at United after a brief spell as interim manager at the end of the 2013/14 season, but insists the club never hinted to him that he would be given the manager’s job permanently.
“No, it was more Louis [van Gaal] who said it,” he said.
“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!’
“Typical Louis. No one else made me any promises. I didn’t think I was ready when I finished playing but, after working with Louis, I felt more than prepared. I know it didn’t work out for United but Louis was brilliant for me because he is a teacher.”
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