Giggs has been Van Gaal's assistant since the Dutchman took over at Old Trafford last summer.
The former United midfielder had a spell in temporary charge of the 20-time English champions following the dismissal of David Moyes last season and Van Gaal believes the Welshman would be the natural choice to succeed him when he departs.
"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."
The Welshman made a record 963 appearances for United during his glittering playing career, which stretched to 25 years.
The 41-year-old won a remarkable 25 trophies, including 13 Barclays Premier League titles and two Champions Leagues.
Just last week Van Gaal spoke of his admiration for the former winger, admitting there was a likeness between him and his own former assistant Jose Mourinho.
''I have to admit, I could not imagine when I spoke with him in May, that he would work so very hard,'' Van Gaal said at a press conference on the eve of United's defeat to Mourinho's Chelsea.
''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 described taking charge of United for four games last year as "the proudest moment of my life".
The former Wales international added: "I have supported Manchester United all my life, I have been a part of the club since I was 13
I am proud, I am happy, a little nervous."
Giggs was given a near-deafening reception when he walked down the touchline and took his place in the home dugout at Old Trafford prior to his first match - a 4-0 win over Norwich.
He was brought back down to earth a week later when his team lost at home to Sunderland, but United bounced back with victory over Hull and rounded off their season with a 1-1 draw at Southampton.
Source : PA