The right-back has been at the Emirates Stadium since 2020, making a total of 44 starts and 15 substitute outings in all competitions.
However, the 31-year-old is very much only regarded as a fringe player by Mikel Arteta at the present time due to the form of Ben White and presence of Takehiro Tomiyasu.
Although Soares recently played the full 90 minutes in a 3-1 defeat to Brighton & Hove Allbion in the EFL Cup, just 30 minutes have come across three outings in the Premier League and Europa League.
The Portugal international still has over 18 months remaining on his contract, leaving the Gunners in no rush to part ways with the player if they wish to keep him as backup for the remainder of the campaign.
Nevertheless, according to ESPN, a number of clubs are preparing to make contact regarding a potential deal.
Fulham are said to be among those teams with Marco Silva likely to be in the market to strengthen his Cottagers squad as they bid to remain in the top half of England's top flight.
Silva is not short of options at right-back with Kenny Tete and Kevin Mbabu in his squad, but Bobby Decordova-Reid has recently been deputising in the role.
Much may depend on whether there is any movement out of Craven Cottage, although Soares would also offer versatility on the opposite flank.
The report adds that Bayer Leverkusen and Villarreal are also ready to monitor any developments with the future of the former Southampton man.
Xabi Alonso will be given the licence to make changes to his Leverkusen squad having recently been appointed as boss, and the same applies to Quique Setien at the Yellow Submarine.
As it stands, Fulham are said to be the frontrunners, with a loan arrangement the most likely outcome if Arteta decides that he is willing to part ways with the experienced full-back.
Soares is allegedly content to stay at the Premier League leaders unless Arteta specifically suggests that game time will remain at a minimum.