The 28-year-old joined the Gunners on loan in January but is yet to make a first-team appearance for the club due to injury and the enforced break resulting from the coronavirus pandemic.
Clubs have until midnight on Tuesday to finalise contracts for the 2019-20 season with those players which run out on June 30.
The situation with Soares is complicated by the imminent expiration of his deal at parent club Southampton.
Due to player registration regulations, Southampton must technically extend his contract first before Arsenal can prolong his loan.
Talks are ongoing on Tuesday with all parties confident an agreement will be reached.
Gunners head coach Mikel Arteta is believed to be impressed by Soares' professionalism and positive impact on the dressing room.
Sources have told ESPN that a three-year deal is under discussion.
The defender is keen on a permanent switch and desperate to make up for lost time having suffered a facial injury in the build up to the resumption of Premier League matches.
Soares' experience is viewed as a useful asset to a squad relying increasingly on young players. He won Euro 2016 with Portugal, featured at the 2018 World Cup and spent last season impressing on loan at Inter Milan, helping the Italian side qualify for the Champions League.
Financial pressures will limit the amount of business Arsenal can conduct in the transfer market this summer but Arteta is hopeful of adding Soares as well as Pablo Mari, the centre-back on loan from Flamengo who suffered a serious ankle injury against Manchester City last week.