The 22-year-old arrived at the Emirates last summer to provide competition and backup to Kieran Tierney, whose injury woes once again sidelined him for a large chunk of the most recent season.
Tavares was therefore thrust into first-team action and made a total of 28 appearances for the Gunners in all competitions, scoring one goal and setting up two more.
The left-back started 13 Premier League games under Mikel Arteta but was substituted early on more than one occasion, most notably against Nottingham Forest in the FA Cup.
Tavares's struggles have supposedly led to Arsenal chiefs considering sending the Portuguese out on loan next season in order to continue his development.
According to Italian journalist Gianluca Di Marzio, Atalanta hold an interest in signing Tavares, who would arrive on a straight loan with no option or obligation to buy.
Di Marzio adds that Arsenal will drive a hard bargain if Atalanta want a permanent deal for the defender, with the Gunners not prepared to accept anything less than €40m (£34.3m).
Marseille have also been credited with an interest in Tavares, with the French club acquiring a number of North London names in recent times, including Sead Kolasinac, William Saliba and Matteo Guendouzi.
Kolasinac's Arsenal deal was terminated in January to allow him to join Les Olympiens, but the Bosnia-Herzegovina international failed to convince and could supposedly be moved on this summer.
Guendouzi will be remaining at the Orange Velodrome permanently, but Saliba has confirmed his desire to make a name for himself at Arsenal, despite Marseille's best efforts to sign him.
Tavares remains under contract at Arsenal until the summer of 2025 with the option of a further year, and the ex-Benfica starlet has eight caps to his name for Portugal's Under-21 side.
Should Arsenal sanction a permanent exit for Tavares, Bologna's Aaron Hickey is being tipped to join the club to compete for the left-back spot with fellow Scot Tierney.
Speculation over a move for Hickey has cooled in recent weeks, though, with Arsenal instead attempting to bolster their midfield and attacking ranks during the summer window.