Tuttosport reports that Conte has been offered a huge four-year contract worth €15 million ($21m) per season by Inter's wealthy Chinese owners the Suning Group.
The former Juventus and Italy boss has allegedly given the green light to this deal after it was raised from €11m.
The paper goes on to claim that a Suning legal team is currently in negotiations with Chelsea owner Roman Abramovich to arrange Conte's release from the London club.
Conte has the Blues sitting 10 points clear at the summit of the Premier League, with the side now heavy favourites to win the title in his first season in England.
Inter, meanwhile, are sixth in the Serie A ladder - 18 points below leaders, and rivals, Juventus.
Results have improved under new manager Stefano Pioli after a wildly inconsistent start to the season under Dutchman Frank de Boer.
