According to Sky Sport, RB Leipzig have agreed a base fee of €25million with Burnley for the French left-footer, with the package capable of rising above €30million through bonuses, plus a sell-on percentage for the relegated Premier League club.
Personal terms with Esteve, who would sign a contract until 2031, were already in place. Despite that deal moving towards completion, Leipzig are also showing interest in Rayo Vallecano defender Nobel Mendy as a further option for the left side of central defence.
The 21-year-old Senegal international, who is also left-footed, is on Leipzig's radar according to Sky, with any move likely to depend on Castello Lukeba or El Chadaille Bitshiabu leaving the club first; Leipzig are said to be willing to sell either player. Mendy is under contract with Rayo Vallecano until 2030 and made 28 appearances in all competitions last season, 24 of them in LaLiga, with his value estimated at around €7.5million.
Leipzig are not the only club interested in Mendy, with Eintracht Frankfurt, VfB Stuttgart and Celtic all showing interest in the defender. Frankfurt have already tried and failed to sign him, having an opening bid of €15million rejected by Rayo Vallecano.
Esteve, meanwhile, becomes the latest player to leave Burnley following their relegation from the Premier League, with the Clarets continuing to lose key personnel as they prepare for life back in the Championship.
Esteve joined Burnley from Montpellier and quickly established himself as one of the club's most consistent performers, but the drop back to the second tier has made a move away all but inevitable.
For Leipzig, his arrival would offer an immediate, ready-made solution on the left of the back line, while any subsequent move for Mendy would represent more of a long-term investment given his relative inexperience at the highest level.
Leipzig's willingness to sanction the departures of Lukeba and Bitshiabu reflects a broader restructuring of the club's defensive options as they look to build a squad capable of competing on multiple fronts next season.