The 23-year-old is expected to become the first Ligue 2 player to move directly to a Championship club in the 21st century.
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A product of the FC Sochaux-Montbeliard academy, Galves made 32 appearances for the club before joining Rodez in 2024.
He quickly became an important part of Didier Santini’s squad, starting 31 of his 36 appearances across all competitions during the 2025/26 campaign.
The Montbeliard-born defender contributed eight assists as Rodez reached the Ligue 1 promotion play-offs.
If the move is completed, Galves will become only the fourth Frenchman to represent West Brom at professional level, following Morgan Amalfitano, Nicolas Anelka and Yann M’Vila.