Eagles boss Ian Holloway has expressed his hope that the 20-year-old might be allowed to stay at Selhurst Park, but Phil Alexander admits he is powerless
Zaha spent the second half of last season on loan at Selhurst Park after completing a £17.5 million move to Old Trafford in January, and played a key role in the Eagles' promotion charge.
Ian Holloway has already publicly voiced his hope that the 20-year-old might be allowed to remain with Palace as they bid for top-flight survival, but Alexander concedes he has little control of the situation.
"It's another option, clearly that's up to Manchester United," he told Sky Sports News. "He's their player now. Will we be asking? We'll probably ask in passing but it's really down to them.
"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."
Whether or not Zaha will be returning, however, Alexander believes Palace have the foundations of a Premier League squad, and insists they will add further quality this summer.
"We're really fortunate - we're coming up with a real good squad," he added.
"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.
"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've looked at the income streams and we'll manage the club the best we can, going forward without taking any risks."
One player Alexander is confident of keeping is Kevin Phillips - the man who scored the penalty which propelled Palace back into the Premier League - even though his contract is up this summer.
"Ian's keen to keep him, there's discussions to be had with Kevin," he continued. "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."