Ramsdale, 26, has made 89 appearances for the Gunners since joining from Sheffield United in 2021 for an initial £24million fee.
The Englishman impressed across his first two seasons at the Emirates, but following the arrival of David Raya from Brentford at the start of the 2023-24 campaign, Ramsdale lost his spot in the team, which has led to much speculation surrounding his future.
The Gunners rejected a loan proposal from Ajax for Ramsdale earlier this month but have still lined up Espanyol's Joan Garcia as his possible replacement.
Meanwhile, Newcastle had enquired about Ramsdale earlier this year but Arsenal's asking price was then deemed prohibitive yet they are now considering lower offers to allow the 26-year old to kickstart his career.
Ramsdale has made 89 appearances for the Gunners, but has fallen down the pecking order
Wolves have offered a loan with option to buy owing to the fact they only have around £20m to spend this window.
Despite Ramsdale's lack of action for Arsenal in recent times, he remained an ever-present in Gareth Southgate's England squads and was No 2 to Jordan Pickford at Euro 2024.
The 26-year-old, who came through the youth ranks at Sheffield United, before moving to Bournemouth, also enjoyed loan spells with Worksop Town, Chesterfield and AFC Wimbledon during the formative years of his career.
Ramsdale was on the bench for Arsenal's 2-0 victory over Wolves on Saturday in their first Premier League game of the season, and the keeper was seen shaking hands with Gary O'Neil ahead of kick off.
Ramsdale's last appearance for the Gunners came in March during a clash against Brentford when Raya was ineligible due to the terms of his initial loan deal from the Bees.