The 20-year-old has impressed during pre-season with the Reds - and while he admits to still being starstruck by the names surrounding him, feels a regular first team berth isn't beyond the realms of possibility.
Although a talent of his own, Zaha will have to first get used to sitting beside Ryan Giggs before making a real impact at Old Trafford.
But perhaps he was being polite when mentioning Danny Welbeck - especially as the two may go head-to-head for a place out wide under David Moyes.
'In the changing room I'm sitting between Ryan Giggs and Danny Welbeck, famous people who I watch all the time on TV,' he said.
'I sit there and think, 'Oh my God, I'm actually in the changing room with these guys'.
'I'm still a bit starstruck, if I'm honest.'
Signed by Crystal Palace in January, Zaha was loaned back to the Eagles for the remainder of the season - which ended in promotion to the Premier League.
That ought to have given the winger - who made his England debut in November - a taste of the big time, something he wants to get used to.
Big time: The winger was loaned straight back to Crystal Palace in January and helped them win promotion to the Premier League
'It's a dream to be able to play with them but I'm obviously here for a reason,' Zaha said.
'I worked hard at Palace to get the move I wanted and I just want to prove to people that I deserve to be here.
'For my first season the plan is to secure a first-team place.
'I just want to be able to play regularly. If I manage to accomplish that then I can move on to other things.'