The Austrian talent has expressed his delight about the speculation linking him to the Italian giant, but remains focused ahead of the upcoming season.
The Nerazzurri asked about the youngster's services, according to the Swiss side's president Bernhard Heusler, and the Austria international has expressed his excitement about a possible switch to the San Siro outfit.
"It is the dream of every player to go to Inter, and I'm no different," the 22-year-old told Corriere dello Sport.
"My agent told me two-three weeks ago that there was interest from Inter, they are a great team with a great history."
Although Dragovic remains focused on the upcoming season in the Super League, he conceded he would have no qualms about a switch to the Serie A outfit.
"At this moment I am only thinking about being in shape for the upcoming season and resuming my training," he said. "However, I must admit, I would be happy if a move went through."
Meanwhile, Heusler revealed the club is in negotiations with the Nerazzurri and have already started searching for a replacement for Dragovic.
"With Inter the deal is not yet complete, but we started to look around for a replacement for Dragovic," the club president said. "It would be unprofessional not to."
Dragovic, who joined Basel from Austria Wien in 2011, still has a contract with the Swiss champion until 2015.