The Blues' desperate search for a new targetman saw them turn to the Bosnia-Herzegovina international in the latter stages of the January transfer window, only to miss out and instead tempt Olivier Giroud to join from Arsenal.
Monchi also confirmed that Giroud was on Roma's radar as they looked for a possible replacement, as was Michy Batshuayi, who headed to Borussia Dortmund on loan from Chelsea.
"We had started talking to Chelsea about Emerson [Palmieri], then they asked about Edin," Sky Sports News quotes him as saying. "We told them to make a bid and we would have evaluate it, but Chelsea never matched the figure we requested and did not reach an agreement with Dzeko.
"We were not 100% convinced to sell Dzeko, but if he had left, a substitute would have arrived. Giroud was an important option, as was Batshuayi. "
Conte admitted earlier this week that he is "a disaster" when it comes to persuading Chelsea to spend big money on players.