The 28-year-old was linked with both Everton and Manchester United during the January transfer window but ultimately remained with Inter beyond the transfer deadline.
Vecino has made 20 appearances for Antonio Conte's side this season and has played the full 90 minutes in their last two Serie A games against Udinese and AC Milan.
However, according to Calciomercato, the Uruguay international is expected to leave San Siro during this summer's transfer window in search of pastures new.
The report claims that Chelsea are still interested in the midfielder, who could be available for €25m (£21m) ahead of the 2020-21 campaign.
Vecino has scored 11 times in 91 appearances for Inter since joining the Italian giants from Fiorentina.