According to information from L’Équipe, Monaco are negotiating with the 20-year-old's representatives despite his current deal running until 2028.
Brunner has emerged as one of the club’s standout performers this season, scoring six goals in seven appearances across all competitions.
His impressive form has attracted attention abroad, particularly from former club Borussia Dortmund, who retain a contractual option to match any offer Monaco receive for the striker.
However, the clause does not give Dortmund priority in negotiations or guarantee Brunner's return to Germany.
Should the Bundesliga club attempt to re-sign him, they would need to reach an agreement with Monaco and convince the player to return.
Meanwhile, Monaco are keen to secure Brunner's long-term future and reward his impressive early-season performances with a new contract.