Lacroix, 26, has been one of the standout defenders in the Premier League since joining Palace from Wolfsburg in 2024, and featured for the club in both their FA Cup victory and their Europa Conference League triumph last season. He has since earned his first France caps and was included in Didier Deschamps' squad for the 2026 World Cup.
Chelsea's interest follows the departure of Marc Cucurella to Real Madrid, leaving Alonso short of options on the left side of defence. The former Real Madrid coach is understood to favour a back three and has identified Lacroix — who has experience in that system — as a player who fits his requirements.
The Blues are believed to be seeking at least two ready-made signings with experience of European football's top leagues, and Lacroix fits that profile. He is one of three or four defensive names under consideration at Stamford Bridge.
Crystal Palace, however, are in no rush to sell. The south London club are under no financial pressure to move players this summer, and are under new manager Pierre Sage following Oliver Glasner's departure. Sage will want to retain the core of a squad that delivered silverware last season.
Palace paid £18m to sign Lacroix two years ago and would expect a significant profit on that investment. Reports earlier this summer suggested the club would demand between €60m and €70m for the Frenchman, whose contract at Selhurst Park runs until 2029 without a release clause.
Liverpool and Bayern Munich had also been tracking Lacroix before Chelsea's interest emerged.