The 26-year-old was spotted in the Saints' end supporting his friend David Brooks during the club's Championship playoff final victory over Leeds United last season.
Ramsdale fell in the pecking order last season under Mikel Arteta after the Gunners brought in David Raya on loan from Brentford.
The England international made just 11 appearances for Arsenal last term and is likely to remain as a backup to Raya in the upcoming campaign after the Spaniard was handed a permanent contract in North London earlier this month.
It is understood that Ramsdale is looking for a move away from the Emirates Stadium this summer in search of first-team football.
Southampton to offer Ramsdale Arsenal escape route
According to The Sun, Ramsdale may now have received an escape route from North London with Southampton reportedly preparing a bid to bring him to St Mary's Stadium this summer.
The report adds that after securing promotion back to the top flight, the Saints are now seeking a top-level, experienced goalkeeper and are ready to step up their interest in the Arsenal star.
It is understood that Russell Martin's side are expected to make a formal bid for Ramsdale when he returns from Euro 2024 with England, despite veteran shot-stopper Alex McCarthy signing a new two-year contract extension with Southampton after his playoff heroics.
The Saints' first-choice goalkeeper Gavin Bazunu is still working his way back to full fitness from an Achilles injury, with Joe Lumley currently serving as McCarthy's deputy.
The Gunners are believed to want to retain Ramsdale's services for the foreseeable future but are willing to listen to suitable offers for the England international.
Newcastle were previously linked with a move for Ramsdale, but the 26-year-old rubbished said rumours before heading to Germany with the Three Lions.
Southampton likely to struggle to meet Ramsdale wage demands
Assuming Ramsdale is open to a move to St Mary's, the major obstacle for Southampton in getting a deal done would be meeting the player's wage demands.
The 26-year-old shot-stopper currently pockets in the region of £120,000 per week with the Gunners, and anything close to that figure would make him the Saints highest-paid player by some margin.
Additionally, Arsenal are believed to be looking to recoup as much of the £30m that they paid for the player when they signed him from Sheffield United in 2021.
However, on the positive side for Southampton, Arteta has previously expressed concerns about complying with PSR demands which could lead to the Gunners considering reducing their asking price for the player to secure a cash deal.
If a suitable offer does not come through, Arsenal might also have to consider allowing the 26-year-old to go out on loan, hoping that his performances would lead to a substantial fee in the future.