Giggs has been assisting Van Gaal since the Dutchman took over at Old Trafford last summer.
The former United midfielder had a brief spell in temporary charge of the 20-time champions following the dismissal of David Moyes last season and Van Gaal – whose current contract runs until 2017 – believes the Welshman would be his natural successor.
“I expect that he (Giggs) will be the next manager after I am gone,” Van Gaal told MUTV.
“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.”
Speaking last week, Van Gaal suggested he could see similarities between Giggs and his own former assistant at Barcelona, Jose Mourinho.
Van Gaal said: “I have to admit, I could not imagine when I spoke with him (Giggs) in May, that he would work so very hard. As an ex-player, you are not used to working hard. He is a very hard worker.
“He reads the game very good, like Jose. But to manage a group you have to learn. What I can see is that he is also learning quickly.”
Giggs, who made a record 963 appearances for United, presided over four matches last season following Moyes’ abrupt departure; winning two games, drawing one and losing the other.??