The former Crystal Palace winger is desperate to make his mark at Old Trafford, having returned from a loan spell at Cardiff, and is keen to start with the club's preseason tour.
Sir Alex Ferguson's last signing before his retirement, Zaha joined United in a 15 million-pound deal from Crystal Palace in January 2013 and was immediately loaned back to the Eagles, helping them secure their promotion to the Premier League.
However, he struggled to make his mark under David Moyes – making just three appearances before his move to Wales – and he is now keen to prove his worth on the club's preseason tour of America, with the Dutchman having replaced the beleaguered Scot.
"It's great to be back," Zaha told United's official website. "There's a nice vibe, everybody's working hard and we're looking forward to the new season. Going to Cardiff was a really good experience for me. I managed to get quite a few games under my belt at Premier League level, which was good, and I feel like I've come back a better player.
"I've realized there are things about my game I need to work on and concentrate on and I know this is the best place to be if I want to improve. I really want to make myself a better player."
United will play LA Galaxy, Roma, Inter and Real Madrid during the tour and Zaha is confident he will be given a chance to show his talent as Van Gaal evaluates United's squad ahead of the 2014-15 season.
"For me, I definitely feel like this is a clean slate," Zaha said. "All I'm trying to do is impress the new manager and get into his squad. All I can do is give my all. There's a new manager and I want to make sure I show him what I can do.
"United are a big club so we need strong opposition and we've got that on pre-season this year. There's no doubt we'll be tested on tour and that's a good thing. It should prepare us well for the season ahead. I’m really looking forward to being involved and I can't wait to face those teams."