Ramsdale started the first four Premier League games of the season before losing his place to David Raya, whose loan move from Brentford will become permanent this summer.
In total the England international has only made six appearances in the league this season, and reports have linked him with a move to Newcastle.
Cole not happy with Arteta over Ramsdale treatment
The 25-year-old joined Arsenal from Sheffield United in a surprise move for an initial £24m in 2021 and has gone on to make 89 appearances for the Gunners.
Former United striker Cole believes a move away from the Emirates could help Ramsdale get his career back on track.
Speaking to The Mirror Cole said: :Nine times out of ten, when a player moves to a different club, they’re meant to be their new club’s number one centre-forward, centre-half, goalkeeper or whatever it may be.
“If Aaron makes the move, he will be Newcastle’s number one goalkeeper.”
It appears that Arsenal will look to sell Ramsdale this summer but Cole isn’t happy with how Arteta has treated the goalkeeper, and believes he didn’t deserve to be replaced by Raya.
“I think [Ramsdale] has been hard done by, I really do,” Cole added.
“He was so good for Arsenal last season and then all of a sudden, Mikel Arteta has gone out and got a new goalkeeper and initially claimed that he had two number ones, which was complete nonsense from day one.
“The way he’s disregarded Ramsdale has been really disrespectful. He’s mugged him off basically.
“I like how he goes about his business and he deserves to be treated with a bit more respect, so if he does move on from Arsenal, then he certainly would do a good job at Newcastle.”
Ramsdale has previously been linked with a move to Chelsea but Newcastle are reportedly leading the race, and the Englishman knows Eddie Howe well from their time at Bournemouth together.