Ivan Perisic has conducted negotiations with Chelsea and a number of other teams about a free transfer after being dissatisfied with Inter's last contract offer, according to reports.
The Croatian's existing arrangement expires at the end of June, and with time running out to reach an agreement, a renewal looks increasingly doubtful.
The Nerazzurri had hoped that Perisic would follow in the footsteps of his compatriot Marcelo Brozovic and sign a contract, but the 33-year-old has been irritated by their approach and the lateness with which an extension has been granted.
Speaking about the situation after a match-winning performance in the Coppa Italia final in midweek, Perisic said: "I don’t know what’s going to happen for my extension with Inter - but you can’t manage the situation like this with important players...you can’t wait until the end."
Perisic's representatives are currently looking for a way out for their client and have spoken with a number of potential suitors, including Chelsea. Juventus, Inter's Serie A rivals, are also interested in signing the dynamic wideman.
However, if a late deal can be struck, a last-minute U-turn to stay at San Siro should not be ruled out, with the player usually pleased in Milan.
Chelsea are interested in Perisic because of his versatility on the left side of the field, particularly as a wing-back. Ben Chilwell will be sidelined until the start of next season as he recovers from ACL surgery, while Marcos Alonso's future remains questionable.