Advocaat, who took over from caretaker manager Ljubinko Drulovic in July after Serbia failed to reach the 2014 World Cup under Sinisa Mihajlovic, is confident both he and Van Gaal will do well in their new jobs.
"It will be a challenge for both of us ," Advocaat told a news conference after naming his 23-man squad for Serbia's friendly against Euro 2016 hosts France in Belgrade on Sept. 7.
"I took this job because like Van Gaal at United, I have a talented group of players blended with experience at Serbia.
"The expectations are huge at both ends but Van Gaal is an outstanding coach and unlike me, he can work with his players every day while he also has some money to buy new players."
Van Gaal has made a dismal start at United and is yet to register a competitive victory, picking up one point from two league games before suffering a 4-0 League Cup rout at third-tier MK Dons.
The arrival of Argentina winger Angel Di Maria from Real Madrid for a British record 59.7 million pounds took United's spending to over 130 million pounds ahead of Saturday's visit to promoted Burnley.
With Serbia also failing to qualify for Euro 2012 after a group-stage exit in the 2010 World Cup, the France friendly will be Advocaat's acid test before he kicks off the Euro 2016 qualifiers away to Armenia and at home to Albania in October.
The 66-year old coach will rely heavily on Serbia's Premier League-based players, with Chelsea's Branislav Ivanovic, left back Aleksandar Kolarov and his Manchester City team mate Matija Nastasic the defensive backbone.
He does also have talented youngsters to choose from, including Chelsea midfielder Nemanja Matic, Southampton winger Dusan Tadic and Liverpool's new signing Lazar Markovic, who faces strong competition to get in the Anfield team.
"It is not ideal that some of my first 11 are not starters at their clubs and I would have also liked more than just one friendly to assess the squad," Advocaat said.
"But five days of practice and the France game should still be enough because I have watched the videos of all Serbia's games in the past two years and have a pretty clear vision where each player will be best used.
"Unfortunately, the quality of Serbia's league is poor and we couldn't pick a single home-based player.
"The good thing is that it gives local youngsters a chance to play regularly and I will keep an eye on the most talented ones as future assets."
Inter Milan midfielder Zdravko Kuzmanovic was the surprise inclusion after he missed Euro 2012 qualifying and Advocaat said he was impressed by the playmaker's pre-season performances.
"He has 46 international caps and played very well for Inter in their U.S. tour so I decided to give him a chance because we need to take a look at all our resources before the qualifiers start," the Dutchman said.
"We will not change the 4-3-3 system but I will make some tweaks to make sure we play more as a team."