Sky Sport Italia is reporting that the Blues have a general agreement in place to bring in the 59-year-old Italian should Conte leave the Stamford Bridge outfit ahead of next season.
However, the same report makes it clear that Chelsea FC are not prepared to pay the £7m (€8m) release clause at Napoli, which expires on 31 May.
Napoli have already announced that they have reached an agreement for Carlo Ancelotti to become their new manager.
According to the same story, Chelsea FC would need to fork out as much as £17.5m (€20m) in compensation if they do decide to part company with Conte this summer.
Conte’s future has been a relentless source of speculation all season due to the Blues’ stuttering form in the Premier League.
The west London club ended up in fifth place in the Premier League table as they missed out on booking a place in the Champions League for next season.
Chelsea FC did win the FA Cup under Conte last weekend as they managed to end the campaign on a positive note.
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