The Netherlands international is out of contract at the end of the season and is yet to secure fresh terms that would keep him at Selhurst Park.
And the Daily Mail reports that Alonso is one of the players being considered to replace Van Aanholt should he leave.
Alonso’s future at Stamford Bridge is in doubt after he fell out of favour under Frank Lampard this season.
The 29-year-old was taken off at half time against West Bromwich Albion in September, with his side trailing 3-0, and hasn’t featured since.
Alonso has another three years left to run on his deal with the Blues, but he isn’t the only name on Palace’s shortlist as Jordan Amavi of Marseille is also said to have piqued the interest of the Premier League club.
However, Roy Hodgson’s side still hope to convince Van Aanholt to pen an extension.
The 30-year-old, who joined Palace from Sunderland in January 2017, is one of several players with deals set to expire next summer.
Jairo Riedewald, Scott Dann, Vicente Guaita, Gary Cahill and Tyrick Mitchell will also be available as free agents unless new terms are agreed.
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