Tomkins came through the Hammers' academy and is hugely popular with the club's fans.
However, the east Londoners' flirtation with a Champions League place this past season could prompt a summer shake-up, as they look to break into the top four next time around, the report claims.
Last week, West Ham were reported by the Turkish press to have lodged a bid for Bursaspor defender Serdar Aziz, despite having an abundance of centre-backs already on their books.
And it appears Tomkins could be the player who makes way, should the Hammers pursue their interest in Aziz or move on to other targets.
Palace, who have been linked with a number of central defenders as they look for alternatives to veteran captain Damien Delaney, are described by the Mirror as being 'interested' in Tomkins, with Sunderland referred to as 'big fans'.
The Black Cats are set to lose Wes Brown on a free transfer this summer, while John O'Shea has only a year to run on his Stadium of Light contract.
Sam Allardyce's men were linked with a move for Feyenoord's Terence Kongolo by Voetbal International on Tuesday.