The Austrian helped the Swiss side to their 16th league title last season, in which they also progressed to the semi-finals of the Europa League before being knocked out by eventual winners Chelsea.
Arsenal, Sunderland, Everton and Southampton were all reportedly tracking the 22-year-old during last season, but Basle club president Bernhard Heusler says his club are now in talks with Inter over Dragovic.
"I feel good at Basle, and in this moment I don't think about other clubs," Dragovic told ITA Sport Press.
"I'd like to play in Serie A and the Premier League in the future. Being linked to Inter pleases me, but I can't know about the future."
Heusler told Swiss paper Basler Zeitung: "Inter are strongly interested in him. Really concrete negotiations have opened."