Italian newspaper Tuttosport claim Inter will offer Conte a four-year deal worth £52million to take over at the San Siro.
The Serie A club will also give Conte a £350m transfer kitty.
Inter Milan want Chelsea boss Antonio Conte as their next manager
Inter are already on their second manager of the season.
The club's new owners Suning Group appointed Frank de Boer at the start of the season, but he has since been replaced by Stefano Pioli.
But Inter's Chinese owners are now looking for a big-name manager and they have set their sights on Conte.
Conte celebrates with Chelsea fans after Hazard scores sensational goal against Arsenal
Sat, February 4, 2017
Antonio Conte was very pleased with Eden Hazard's goal against Arsenal!
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Antonio Conte has helped Chelsea move 12 points clear at the top of the Premier League table
The news will come as a blow to Chelsea, as Conte has been hugely impressive at the west London club this season.
Conte has guided the Blues to the top of the Premier League table, and they are now 12 points clear following yesterday's 3-1 victory over Arsenal.
Conte has experience of working in Serie A before, having won the league three times in a row with Juventus before leaving to take over as coach of the Italian national team.