Giggs is now Louis van Gaal's assistant boss.
"I have always said that Giggsy has this streak running through him that you see in top managers," Beckham said.
"I saw him as a player, he is so determined and when you have someone who is from this part of the world and from this club that means so much to the fans.
"I hope at some point that Giggsy does take over. It might not be for five years or 10, but I hope he does."