Stoke paid a club-record fee to sign the Frenchman from Porto in February 2016, but he has failed to justify the £18.3m fee which was paid for his signature.
That has led to the 24-year-old being made available for transfer, but according to chief executive Tony Scholes, the Potters are still awaiting a concrete offer.
"It's that time of year, we are still very early," he is quoted by the Stoke Sentinel as saying. "The only deals that tend to get done this early are the ones where things were put in place before, or where the player is a free agent and you haven't got the complication of having to deal with the club, you are just dealing with one party.
"There's been one or two high-profile ones done, but there hasn't been that many deals done between clubs to buy or sell a player, yet. So we are a little bit early and on Giannelli, as with a number of players, everything is just speculation at the moment."