The French club have suspended Villas-Boas and want to replace him immediately.
However, Sky Italia reveals Sarri turned down the club's approach, and the 62-year-old does not want to manage until the start of next season.
Marseille are also being linked to ex-Borussia Dortmund boss Lucien Favre, along with Leonardo Jardim and Ernesto Valverde.
The club sit in 9th place in Ligue 1 after 21 games, and they have played two less than most of the teams above them in the table.
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