Dzeko has been heavily linked to a move to Chelsea, with Sky Sports and The Guardian both reporting earlier in the day that a deal had been agreed.
But speaking ahead of his side’s Serie A clash at Sampdoria, Monchi denied that any deal had been struck.
“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,” Monchi told Mediaset Premium.
“We are ready to listen and then we decide. Now Dzeko is here and the rest doesn’t matter, which means what we’ve received so far wasn’t acceptable.
“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’ve gone to sign Leo Messi.
“We must win to change the dynamics of the last few games. We had a good performance against Inter and today need an even better one.”
Dzeko started Roma’s game and scored a stoppage-time equaliser to secure a 1-1 draw.