Speaking at a charity event, Sharpe said that he never expected to see Giggs in the Old Trafford dugout when they were both teenagers, but now believes that the Welshman is being groomed to take the reins after Van Gaal.
"For me, it's an ideal scenario," Sharpe is quoted as saying by the Manchester Evening News. "The new manager comes in, does three, four, maybe five years depending on how it goes. I think after that, Giggsy will be the man to take the job on.
"Giggsy has matured over the years, he speaks well, he knows the game inside out and he's played at the highest level.
"He understands the players. He's not one to rant and rave, he'll talk to people and help them improve their game."
Giggs managed two wins, one draw and a defeat when he took over from David Moyes as interim manager after the Scot was sacked last season.