Inter's Chinese owners were hoping that they could convince Conte to move back to Italy as it is well known that the Chelsea manager was missing his family, despite his impressive first season at Stamford Bridge.
Conte was also linked with Barcelona this week after Luis Enrique announced he would leave the club at the end of the season, but sources have told Goal that the Italian was never seriously considered.
Chelsea are 10 points clear at the top of the Premier League table with 11 games left to go, but Conte admitted last week that he misses his wife Elisabetta Muscarello and his daughter Vittoria, who have so far remained in their native country as he adapts to London life. They are expected to join him in England over the summer.
Conte's current contract runs until June 2019 and he has reiterated his desire to remain at the club in recent press conferences at Cobham Training Ground.
Inter are expected to eventually appoint Atletico Madrid's Diego Simeone as coach after he played for the Milan giants in the 1990s.
However, in recent weeks, it is believed that the Suning Holdings Group leadership at the club were sounding out Conte as their first choice ahead of the Argentinian.
Conte, though, now looks ready to quash all speculation about his future by agreeing a new deal with runaway Premier League leaders Chelsea.