CEO Karl-Heinz Rummenigge says World Cup winner remains "unsellable" despite poor 2016-17 season.
Goalkeeper's switch to Turin could eventually be worth €15.3m.
Previous reports suggested OM were confident of sealing €28m deal for French international.
Chile international has less than 12 months remaining on his contract.
Lemar has been among Monaco's best players last term.
Craig Shakespeare insists no decision to be made over wantaway Foxes star with no offers submitted.
Karl-Heinz Rummenigge says Bayern have little need for another attacking player.
Arsenal have signed two players in the summer transfer window so far – Kolasinac and Lacazette.
Sanchez has already expressed his desire to play in the Champions League.
Arsene Wenger wants Celtic forward Dembele to replace Sanchez if he leaves The Emirates Stadium.
Monaco reportedly unwilling to let another player leave the club this summer.
Arsenal have made two signings thus far in the window.
Crowley has not made a single first team appearance for Arsenal.
Kolasinac and Lacazette both played in Arsenal's pre-season friendlies.
A move to 4-4-2 and Cristiano Ronaldo's retention means there is no place for the teenage sensation.
"There is no speculation - no matter what happens he will stay," says defiant Gunners boss.
Baars' father confirmed the 16-year-old was wanted by Chelsea and Arsenal.
Sanchez's contract expires in the summer of 2018.
Gunners boss says club have made no offers for French teenager, who he expects to stay in the principality.
Sampdoria have joined West Ham in the race to sign injury-plagued 25-year-old.
Wenger has signed a two year extension at club.
The Leicester City winger wants to leave the 2015-16 Premier League champions.