Giggs has been placed in charge of the team until the end of the season following the sacking of David Moyes.
After last week's 4-0 win over Norwich, there is a growing sense within the United dressing room and among the club's vast fan base that Giggs should be allowed to carry on as manager beyond the summer.
The United board regard Giggs as a potential manager of the future, but they are expected to appoint Louis van Gaal as their next boss instead as he has far more experience.
But Saha, who played alongside Giggs for four years, thinks the Welshman is good enough for the position now.
Speaking at the launch of the Soccerex global convention in Manchester, Saha said: "He can do the job now, for sure.
"It seems like an easy choice for now because he proved he can do it last weekend.
"I was sad to see David Moyes go. But maybe it would have been more clever to give (Giggs) his chance months ago."
Giggs is yet to complete his UEFA Pro License, but Saha thinks that should not prevent the 40-year-old from being a successful manager.
Saha believes Giggs has already gained a wealth of knowledge from the 23 years he spent working under Sir Alex Ferguson.
"The foundations are there (for Giggs to be a success). He was learning from the best," Saha said.
"I could see that in the dressing room. The charisma was there when he was a player. You could feel that straight away.
"He has the right character. He could have a laugh and a joke but he also kept his distance sometimes.
"He has the pedigree and the biggest weapon he has is that he knows exactly what the fans are after - that they want the team to play the United way.
"He was an attacking midfielder so he knows they want to see dribbling and counter-attacking football."
The hallmarks of the 'United way' were present during last week's demolition of Norwich.
And Giggs is doing all he can to make sure there is a repeat performance when United host Sunderland on Saturday afternoon.
It is understood that Giggs has introduced double-training sessions at the AON Training Complex to make sure his players are up to speed for the game.
By the time the next game comes around against Hull on May 6, Van Gaal may have been appointed as Moyes' successor.
The Dutchman is keen to finalise his contract at Old Trafford before he gets his Holland squad together for their training camp on May 7.
United are keen for Giggs to stay at Old Trafford in some capacity, but they will not force the new manager to include the club's record appearance maker among his backroom staff.
Whoever takes charge next year, they will have to do far better than Moyes, who left United seventh in the Barclays Premier League just a year after Ferguson won the title by 11 points.
Saha firmly believes the club will bounce back and start challenging for honours provided the new manager spends big in the transfer window.
"You have to bring players in and if those players are the right ones then they will definitely bring success back to the club," said Saha, who two Premier Leagues, one Champions League and one League Cup during his four-year spell at Old Trafford.
"When we bought Robin van Persie (in 2012) he was a big signing, he lifted the club and he won us the league and this is what one signing can do.
"People talk about money and say this is destroying the game but money talks."