The young midfielder has attracted attempts from Lazio and Napoli already this month.
Gemmi has confirmed an offer from Lazio, which fell short.
He told Sky Italia: “We were not expecting it, but this is what happens in transfer negotiations and it is only right that each club looks after its own interests.
“We were not actually far away from an agreement on the figures and the player was convinced too, but the formula was the big problem and that saw the whole operation collapse.
“Napoli also had interest and made an offer, which was a little higher, but we never got into the same specifics as we did with Lazio.
“Fazzini preferred going to Lazio rather than Napoli too. The issue was mainly the formula of the transfer, whether it was a loan with option or obligation, there are certainly technical issues both clubs needed to take care of and requirements for the balance sheet.”
Gemmi continued: “I never close the door permanently on any negotiation, but I will admit that it is unlikely at this stage.
“The player is a great professional and it was me and the coach who decided to leave him out for the most recent match so he could relax and decompress a little.
“Fazzini is already back in training and ready to resume with Empoli. He is a product of our academy, we’ll see how it all develops, but after two or three shaky days, he will get back on track.”