The Belgian winger, who scored a stunning volley against Panama in his country's opening match of the World Cup, is being lined up by his former manager for a switch to the Premier League.
Sarri, who has still not replaced Antonio Conte, could be announced as the new coach at Stamford Bridge by the end of the week according to the Daily Mail.
Conte and his staff have still not agreed a compensation fee with the club, and Napoli who still employ the Italian despite Carlo Ancelotti replacing him in the managerial position, are asking for a fee of £3.5 million to release Sari from his contract.
However, should the necessary arrangements be made for the change in manager to occur, the coach would aim to add the player, who scored 21 times for his Napoli side last season, to the Blues' squad.
Mertens did have a £24 million release clause in his contract but that has now expired, which means that acquiring the 31 year-old winger could cost a lot more.
Sari seems to be wanting big changes at Chelsea, with the likes of Anthony Martial and Jean Michael Seri also on the Italian's radar.