The 23-year-old Toulouse defender has stayed on Palace's shortlist since their initial interest during the January transfer period, with that admiration now carried into the off-season.
Cresswell, formerly of Leeds United and Millwall, has developed significantly since moving to France in 2024, racking up 66 appearances for Toulouse and establishing himself as a regular starter. He also has 26 caps for England U21s, highlighting his standing at international youth level.
Palace's renewed focus on defensive recruitment has been driven in part by the failure to directly replace Marc Guehi following his January move to Manchester City.
That departure left a void in the back line which the club are now prioritising addressing, with at least one centre-back addition viewed as necessary amid possible wider defensive reshuffles.
Interest is not limited to Cresswell, however. Chelsea have recently made an enquiry regarding Palace defender Maxence Lacroix, a development that has prompted further internal consideration of squad depth and potential turnover in central defence.
Beyond defensive targets, Palace are also tracking Lens midfielder Mamadou Sangare. The player is known to head coach Pierre Sage from a previous working relationship, which could aid evaluation if negotiations progress.