Giggs has been working as Van Gaal's assistant since the former Barcelona boss took over at Old Trafford last year.
The United legend had a spell in temporary charge following the dismissal of David Moyes last season and Van Gaal believes Giggs would be the ideal choice to replace him in the long-term.
"I expect that he (Giggs) will be the next manager after I am gone," Van Gaal told MUTV on Friday.
"Now I have the responsibility. He has tasks that he has to perform like the players. What he has to do, for me, he does it very well."
The 41-year-old won a remarkable 25 trophies, including 13 Premier League titles and two Champions Leagues.
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