Manchester United turned down a late attempt from Palace to re-sign England international Zaha during the summer transfer window, according to the Daily Star.
The 20 year old made 126 league appearances in just over three seasons with the Eagles, and became Sir Alex Ferguson’s final signing for United back in January.
He was loaned back to the London club for the second half of last season, and played a key role in their return to the top flight.
His only appearance so far for the Premier League champions came in the 2-0 Community Shield victory over Wigan Athletic at Wembley a month ago.
He won his second full international cap that same week, while he was also part of the U21 squad for the recent 2015 European Championship Qualifying double header against Moldova and Finland.
Earlier this week, England U21 manager Gareth Southgate assured Zaha of his place in future squads regardless of how much game time he gets with David Moyes men this season.