Tavares joined Arsenal last summer from Portuguese giants Benfica, and struggled to nail down a starting spot under Mikel Arteta in his debut campaign.
The full-back made only 13 starts in the Premier League last term and has been linked with leaving the club just one season following his arrival.
Serie A outfit Atalanta, who are long-term admirers of Tavares, are keen on taking him to Italy in the ongoing window, while he was the subject of an enquiry from Ligue 1 giants Marseille recently.
And according to French outlet Foot Mercato, Les Phoceens have acted upon their interest and tabled a loan offer for the Arsenal star.
Marseille want to sign Tavares on an initial temporary basis with an option to make his move permanent.
Arsenal are yet to respond to the Ligue 1 outfit but they are open to the idea of sending Tavares out on loan this summer.
The 22-year-old is expected to deputise for Kieran Tierney at left-back should he stay at the Emirates Stadium for next term, while Marseille, who are in the Champions League could offer him regular game time.