The 22-year-old arrived at the Emirates Stadium from Benfica last summer and ended his debut year at Arsenal with one goal and two assists from 28 outings in all tournaments.
Tavares made 22 appearances in the Premier League during Kieran Tierney's injury-forced layoffs, starting 13 of them and scoring his first goal for the club against Manchester United.
However, the Portugal Under-21 international was criticised for some below-par defensive displays and was memorably taken off in the first half of the Gunners' FA Cup third-round loss to Nottingham Forest.
With Tierney set to return from injury in time for the start of the new season, Arsenal are said to be considering the possibility of a loan move elsewhere for Tavares.
According to French outlet Foot Mercato, Marseille - who were previously reported to hold an interest in Tavares - have now approached Arsenal with a loan offer for the defender.
The report adds that Marseille's proposal also includes an option to buy, and Arsenal are yet to respond to the Olympiens' request, but a straight loan deal would be acceptable to the Gunners.
Atalanta BC chief Lee Congerton has also revealed that his side hold an interest in signing Tavares, whose contract with Arsenal does not expire until the summer of 2025.
"I've followed Tavares since he was playing for Benfica's youth team, he's a strong player. But Tavares is under contract with Arsenal - and it's really difficult to sign players from Premier League clubs," the Evening Standard quotes Congerton as saying.
Should Marseille try to strike a permanent deal for the left-back, Arsenal would supposedly be after a €40m (£34.5m) fee to let Tavares leave for good.
A number of Arsenal players have crossed the English Channel to Marseille in recent times, with another left-back in Sead Kolasinac joining in January after terminating his contract at the Emirates.
However, Jorge Sampaoli often overlooked Kolasinac for starts last term, and the Bosnia-Herzegovina international is at risk of being let go by the French giants after just six months.
Matteo Guendouzi's move back to his homeland was a successful one, and the midfielder will complete a permanent move to the club - ending a four-year stay at Arsenal in the process.
William Saliba won the Ligue 1 Young Player of the Year award for his performances at the Orange Velodrome last season, but the centre-back has already confirmed that he wants to stay at Arsenal, where he has not made a single first-team appearance in three years.
Arsenal continue to search for attacking reinforcements in spite of Eddie Nketiah's contract renewal, and a verbal agreement has allegedly been reached with Manchester City over a deal for Gabriel Jesus. body check tags ::