Van Gaal, 64, was appointed to the job last year and has said on more than one occasion this season he will leave and retire in 2017.
Giggs, 41, has played more matches for United than anyone in their history, bringing his 23-year playing career to an end in 2014.
He is currently working as Van Gaal's No.2 and Beckham told Talksport radio on Friday he had no doubt that his former team mate and "Class of 92" graduate will make a success of the job if he takes it.
"He is manager material. He’s got that streak that runs through him that you need to be a top manager.
"He has learnt from Sir Alex Ferguson over the years, he is learning from Van Gaal now. He is taking his time, doing all the right things, and without a doubt all Man United fans would like to see Giggsy, at some point, be manager of Manchester United.
"To have played for the club the amount he has and have that appreciation and understanding of how Manchester United is, he would be perfect at some point to step in."
Beckham, 40, who played with Giggs for United from 1992 until 2003 will return to Old Trafford on Nov. 14 to play for a Britain & Northern Ireland XI, managed by Ferguson.
They will play a Rest of the World XI managed by Carlo Ancelotti and captained by Zinedine Zidane with proceeds going to United Nations children's agency UNICEF.
(Reporting by Mike Collett; Editing by Amlan Chakraborty)
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