However, the situation isn't straightforward. Chelsea do not want to pay Sarri's £7million (€8m) release clause, which expires on May 31.
The aforementioned media source suggests this is because the 'Blues' would need to pay Conte £17.5m (€20m) in compensation if they decided to part ways with the Italian.
Even after Sarri's expiration date, clubs wanting to secure his services will still need to negotiate with Napoli owner Aurelio De Laurentiis, creating another sticking point.
If the situation doesn't sort itself out, Chelsea will turn their attention to Fulham boss Slavisa Jokanovic, who won promotion to the Premier League on Saturday.