The Red Devils are two points clear of fifth-placed Liverpool after a 3-0 win against Tottenham Hotspur at Old Trafford on Sunday.
Van Gaal has been criticised in recent weeks after United crashed out of the FA Cup after a 2-1 defeat by Arsenal in the quarter-final at Old Trafford.
However, Bogarde, who played under Van Gaal at Camp Nou, is confident that the 63-year-old manager can restore United to their former glory.
Bogarde told talkSPORT: “Manchester United is a very big club and he has a lot of experience working at big clubs. It is not an easy job, but he has the experience and we have to give him some time to do his work.
“I am very confident he will be successful at Man United. You can see they are playing better each game, so I am confident they will get a Champions League ticket for next season.”
Van Gaal was named as David Moyes’ permanent successor in May, penning a three-year deal with the 20-time English champions.
United make the short trip to top-four rivals Liverpool in the Premier League on Sunday, looking to move five points clear of the Merseyside outfit.
The Red Devils have won their last three Premier League games against Sunderland, Newcastle United and Tottenham.
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