The Crystal Palace talisman joined United from the Eagles for £10million back in 2013.
But Zaha made just four first-team appearances at Old Trafford, getting more game-time on loan at Cardiff City who were then managed by current Manchester United boss Ole Gunnar Solskjaer.
Zaha returned to Palace on a permanent basis in February 2015 for a fee thought to be worth up to £6m.
The 26-year-old has grown into the south London club’s most important player with his contributions in the final third vital to their safety.
The Ivorian international hit a career-best 10 Premier League goals in the season just finished while adding 10 assists to be directly involved in a little under 40 per-cent of his team’s goals.
Zaha is understood to have told Palace that he wants to leave the club in order to play Champions League football and compete regularly for trophies.
Former employers United are among the teams linked with a summer swoop for Zaha but ESPN FC’s Steve Nicol suggests the forward will look to go elsewhere because of how tough a time he had in his previous spell with the Red Devils.
“I think the time is right for him to take a step up,” Nicol said of Zaha, who signed a five-year deal last summer worth £130,000-a-week at Selhurst Park.
“I don’t believe he’s the type of player or person who wants to go abroad, I think he’s quite happy in England.
“He’s already had that stint at Manchester United, which was a complete disaster and was probably part of his maturation.
“Because he’s been there already, there’s been links to United. I don’t see him doing that.
“I don’t think, psychologically, having had such a disaster there for two seasons that he would go back so we can forget them.
“I think we’re talking Arsenal or Chelsea. If Chelsea are letting [Eden] Hazard go, they will still be able to make some transfers.
“Arsenal, I’m not keen on what they have in wide areas. [Alex] Iwobi, for me, in the final third has no end product and [Henrikh] Mkhitaryan has had an absolute disaster.
“I think they would like him and both sides would suit him.
“I think every player wants to go to the best but for him, he thought he was going to the best before and it didn’t work out.
“I don’t think it’ll be a case of going to the best side, it’ll be a case of going where you’re going to play.”