Monchi has admitted his side would entertain offers and accepts that every player has their price.
But the low-ball bid from Stamford Bridge was of no interest at all to the Serie A side.
He said: “Roma, like every club in the world, listen to the offers that arrive for their players, not just for Edin, but anyone in the squad.
"Every club in the world would at least consider any offers that come in. We are ready to listen, and then we'll decide.
“We are ready to listen and then we decide.
“Now Dzeko is here and the rest doesn't matter, which means the offer that arrived is not interesting.
“I don't know what personal terms were offered to the player, as I am not his agent.
“I am talking about Roma: an offer arrives, we look at it and then decide.
“A director of sport must look at the economic and sporting aspect, that is the point of the role.
"I am a director, I must consider both, otherwise tomorrow I would go to sign Leo Messi."