The 20-year-old joined the Premier League champions in January, but he was immediately loaned back to Palace where he went on to help Ian Holloway's side to promotion via the play-offs.
Questions have been frequently asked as to whether Zaha will return to his former club for the forthcoming season, but Alexander says that any potential deal would be in United's hands.
"It's another option, clearly that's up to Manchester United. He's their player now. Will we be asking? We'll probably ask in passing but it's really down to them," he explained to Sky Sports News.
"Would we love to see Wilfried back? Of course we would but he's got a career at Manchester United and, after a few training sessions up there, I'm not sure they'll be willing to let him out on loan."
Palace are returning to the top flight after an eight-year absence and they have already been linked with signing a host of names, but Alexander was cautious about any new arrivals.
"We're really fortunate - we're coming up with a real good squad," he said.
"Most of our squad from last year is signed up, they're obviously used to playing with each other, they've got great team spirit and we will be adding to the squad.
"There's a number of names on the list but we've already got the basis of the squad already there. It's difficult to say in terms of numbers - we have got some key areas.
"We did have an injury to Glenn Murray at the back end of last season and he was our top goalscorer so it's pretty clear that we need a centre-forward and probably two or three more to add to the squad.
"We're in no major rush, we've got some good targets, Ian's done a lot of homework in terms of what players are available and we're now talking to various agents, talking to other clubs and going through that process.
"We've got a budget in mind, it would be daft to give out numbers but we've worked out the budget.
"We've looked at the income streams and we'll manage the club the best we can, going forward without taking any risks."
Veteran striker Kevin Phillips scored the goal which sealed Palace's promotion, and Alexander added that the club are looking to offer the former Sunderland man another season.
"Ian's keen to keep him, there's discussions to be had with Kevin. Even at 40, I still think he could do a job in the Premier League from being part of the team. He's a great guy to have around.
"Could he come on and do a job in the last five, 10, 15 minutes of a game? I'm sure he could.
"Those discussions will be had and I'll be hopeful that he'll sign a contract with us."