According to Ouest-France, the two Ligue 1 clubs have reached an agreement worth around €25 million for the 23-year-old defender.
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Cresswell had also attracted interest from Crystal Palace, but Rennes had already agreed personal terms with the player.
Rennes were seeking a young yet experienced centre-back following the departure of academy graduate Jeremy Jacquet, who joined Liverpool for a club-record €72m fee.
Cresswell’s impending arrival represents another statement of ambition from Rennes, who have added several Ligue 1-proven players this summer, including Adrien Thomasson and Issa Soumare.
Franck Haise’s side will also compete in the UEFA Europa League next season, making defensive reinforcements a priority.