The Eagles were already forced into selling Marc Guehi to Manchester City for just £20 million in January as his contract was set to expire in June.
But Steve Parish has more control when it comes to resolving Lacroix's future, as the towering French centre-back is under contract at Selhurst Park until 2029.
That explains why Palace now value Lacroix at around £50 million - according to TEAMtalk - who have also revealed that the South London club are willing to offer him an "improved contract".
Lacroix's development into one of the Premier League's best defenders has resulted in interest in major clubs, including divisional rivals Chelsea and Liverpool.
A new contract for the 26-year-old - who was recently named in Didier Deschamps' France squad for the 2026 World Cup - would be a huge statement of intent from Palace ahead of their Europa Conference League final against Rayo Vallecano on May 27.