Zaha is free to open talks with foreign clubs over a pre-contract agreement as his contract at Selhurst Park runs until June 2023.
The Ivory Coast international is believed to be attracting plenty of interest in the UK and abroad.
Arsenal, Chelsea and Tottenham Hotspur are among the Premier League clubs credited with an interest in the Ivorian, who has scored six goals and registered two assists in 15 top flight appearances this season.
Fichajes claims that Barcelona have earmarked the 30-year-old attacker as a potential replacement for Ferran Torres, whose future at the club is uncertain.
Torres has quickly fallen down the pecking order at Camp Nou and has only started six top flight games in the 2022-23 season.
The Spain international is under contract at the Blaugrana for another four and a half years.
Meanwhile, Zaha represented the Eagles at the youth level between 2004 and 2013 before joining Manchester United, where he made just four senior appearances.