Giggs was placed in temporary control at United following David Moyes' sacking last month, less than 12 months into a six-year deal.
United's first match under the veteran Welsh winger was a comprehensive 4-0 win over Norwich City on Saturday and he will be in charge for the club's remaining three fixtures this season.
Netherlands coach Louis van Gaal has been heavily linked with the permanent job, with Giggs potentially becoming part of his backroom staff, but Saha called for his former team-mate to be given a chance.
"I know Ryan's relishing the chance and I think he deserves a chance," he told Sky Sports News.
"It's a great opportunity for him. He definitely has the quality, he has the character, the strength and the charisma. There's no doubt about that.
"Experience is the only thing that is missing from him but you know when you play more than 20 years at Manchester United you know how to work, you know exactly how to behave.
"I may be wrong, but I think it's a bit sad, maybe he could have been given a month more to settle, to prove to people he's the right choice. Four games is not enough, I think."
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