It's understood the Blues were willing to pay the German giants around £10m for his services but Demichelis has opted instead to stay and fight for his place in Louis van Gaal's side.
Demichelis has been interested in a move to Sevilla but that deal collapsed after they failed to meet Bayern's asking price.
van Gaal is willing to let the 29-year-old go, but the defensive midfielder turned centre-half said: "I will be very honoured to stay at Bayern and fight.
"The coach gave me his reasoning and he said I had a hard decision to make, but I've accepted it already and there was mutual agreement."
Bayern have also ruled out the possibility of a loan deal for the player, despite not guarenteeing regular first-team football.