Former Porto, Chelsea and Tottenham boss Villas-Boas has impressed since succeeding Rudi Garcia at the Stade Velodrome last May and guided Marseille to a second-place finish in the truncated 2019-2020 Ligue 1 season.
At the start of this month, the 42-year-old sought assurances over what transfer funds would be available to improve the squad, while the departure of sporting director Andoni Zubizarreta last week cast his position into fresh doubt.
RMC Sport reported on Tuesday that Villas-Boas had rejected a one-year extension to his deal, which runs until June 2021.
However, Marseille issued a statement to clarify they were awaiting an response to an offer of two more years, plus an additional 12 months dependent upon Champions League qualification.
"Following erroneous information in the media recently concerning the contract extension proposed to Andre Villas-Boas, Olympique de Marseille wishes to re-establish the reality of facts," a club statement read.
"As early as last week, the president of Olympique de Marseille, Jacques-Henri Eyraud, spoke with Andre Villas-Boas about his desire to offer him a contract extension.
"Over the weekend, [Marseille owner] Frank McCourt confirmed to Andre Villas-Boas that he was on the line with Jacques-Henri Eyraud and hoped that they would both work on the terms of this extension.
"At the end of the day on Monday, the club sent Andre Villas-Boas a proposal to extend the contract by two years (for the 2021-22 and 2022-23 seasons) plus one optional year (2023-24), if OM qualified for the Champions League that year."
Marseille went on to detail the ructions brought about by frequent coaching changes in recent decades, which have yielded a sole Ligue 1 title in 2009-10 since their 1992-93 Champions League triumph.
"For 20 years Olympique de Marseille has been a club that has suffered chronic instability. Twenty-four coaching changes have been issued by OM during this period," the statement continued.
"Over these 20 years, only three coaches have received a contractual commitment of 4 years or more: Didier Deschamps, Rudi Garcia and today Andre Villas-Boas with this proposal.
"First of all, this shows the club's desire to create conditions of stability. This also demonstrates the determination of the club to invest when it deems it necessary in the conditions of sporting success.
"Finally, this demonstrates all the confidence the club has in the technical qualities of Andre Villas-Boas, with whom Olympique de Marseille wishes to write an important page in its modern history."