The Bundesliga side are seeking defensive reinforcements amid the expected departure of Castello Lukeba, who is attracting interest from several top European clubs, and have identified the former Montpellier centre-back as a priority target.
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Personal terms are not expected to be an issue, with the player said to be open to the move.
Esteve joined Burnley in February 2024 and has since become a key figure in the squad, starting all 36 of his appearances during the 2025–26 season, despite the club’s relegation to the Championship.
The 1.93m French defender, a former Under-23 international, could now be set for a switch to Germany, where Leipzig’s Champions League qualification adds further appeal to the potential transfer.