The 23-year-old has impressed since joining Toulouse from Leeds United for €5 million in 2024, establishing himself as a key player under former head coach Carles Martinez Novell.
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Rennes have tracked the England youth international throughout the past season, but Crystal Palace are also in the race as they prepare for the possible departure of Maxence Lacroix to Chelsea.
Toulouse are expected to demand at least €25 million for Cresswell. While the Ligue 1 club may need to sell to balance their finances, they are determined to secure a significant fee for the highly-rated centre-back.