Ramsdale has fallen down the pecking order under Gunners boss Mikel Arteta since the arrival of David Raya from Brentford last summer.
The 25-year-old has subsequently been reduced to just 10 first-team appearances across all competitions this season, including only five outings in the Premier League.
Ramsdale has not played in the top flight for Arsenal since the 1-0 win at Brentford on November 25, when Raya was ineligible to face his parent club, while his last appearance between the sticks in any competition was in a 2-0 home defeat to Liverpool in the FA Cup on January 7.
Raya is set to make his move to Arsenal permanent for a reported £27m this summer, and having snatched the No.1 jersey, speculation over Ramsdale's future has since surfaced.
Although Ramsdale still has over two years remaining on his contract at the Emirates Stadium, a recent report claims that the shot-stopper is ready to leave the Gunners this summer in search of regular game time.
Arsenal, meanwhile, have reportedly identified Ajax's Diant Ramaj as a potential replacement for Ramsdale, with the 22-year-old valued in the region of just €15m (£12.8m).
Multiple Premier League and European clubs are believed to be closely monitoring the Englishman's situation, with previous reports crediting London rivals Chelsea with an interest.
Indeed, the Blues allegedly weighed up the prospect of luring Ramsdale to Stamford Bridge during the January transfer window when first-choice goalkeeper Robert Sanchez was nursing a long-term knee injury.
According to 90min, Ramsdale is set to make a decision on his Arsenal future after Euro 2024, but Chelsea are not expected to enter the race for his signature contrary to previous reports.
The report adds that the West Londoners are satisfied with their current goalkeeping options in the form of Sanchez and Djordje Petrovic, while 19-year-old USA international Gabriel Slonina - who is currently on loan at Belgian outfit Eupen - is set to return this summer.
It is also claimed that Chelsea will instead prioritise the addition of a new centre-forward this summer, as well as a new centre-back, full-back and potentially a midfielder if Tottenham Hotspur-linked Conor Gallagher were to leave the club.
Mauricio Pochettino began the 2023-24 campaign with Sanchez as his first-choice goalkeeper; the Spaniard joined Chelsea from Brighton & Hove Albion last summer for around £20m and has since made 20 appearances in all tournaments.
Sanchez picked up a knee injury in mid-December which allowed Petrovic to take his place between the sticks, starting 16 games in all competitions before returning to the bench on Wednesday as Chelsea beat Leeds United 3-2 in the FA Cup fifth round.
Both Sanchez and Petrovic will continue to battle with each other as they bid to start for the Blues in Saturday's Premier League trip to Brentford.