The Montenegro forward scored twice against Liverpool in the Champions League back in 2009 and the Reds have been monitoring his progress ever since, reports suggest they may now be considering a move in the New Year.
The 21-year-old is also wanted by both Arsenal, who had a last minute bid last month rejected, and Chelsea. But, with reports suggesting he is holding out on his new deal, it could be that he is on the move in the new year.
"It's not only Chelsea who want Jovetic, but Arsenal also," former Fiorentina defender Roberto Galbiati told Italian television station Italia 7.
"Arsenal, on the last day of the summer transfer market, submitted a bid to Fiorentina but the club refused."