The two Premier League sides are keen on signing the Fiorentina striker in January, having missed out on him in the summer.
The 21-year-old has caught the eye at the start of this season, with six goals in seven appearances for the Serie A outfit.
Fiorentina president Rocco Commisso has now admitted to TuttoMercato that he is unsure whether Vlahovic will commit his future to I Viola.
"I do not know if he will sign, we are calm," Commisso said. "We have been working on it for months, one day we are positive, others less."
Commisso added that Fiorentina have offered the Serbian striker a record-breaking salary, stating: "He's taking a big risk, I told him. We offer him a five-year contract at 40 million euros gross. The thing I say is that it would be the largest figure ever given to a Fiorentina player, including Batistuta and Rui Costa."
Vlahovic joined Fiorentina from Serbian side Partizan in 2018.