The 30-year-old left-back has now entered the final year of his contract at Selhurst Park and the Eagles want to lock him down for longer.
The club have put an initial offer on a new contract to the Dutchman, but it appears there is still work to do before he accepts.
No decision has been made on him putting pen to paper and it is claimed that talks are likely to continue beyond the initial proposal.
Van Aanholt made 29 appearances in the Premier League for Roy Hodgson’s side last season and chipped in with goals against Manchester United, West Ham United and Newcastle United.
The 30-year-old is likely to be keen to make sure the next contract he signs is the right one as it could be his last big deal given his age.
Crystal Palace snapped up Van Aanholt from Sunderland in 2017.
The left-back has so far won ten caps at international level for the Netherlands.
