Ramsey, 27, will end his ten-year association at the end of the season after contract talks were ended by the Gunners last month.
With 60 goals and as many assists in 340 appearances since joining the club from Cardiff City as a teenager, his former teammate Jack Wilshere feels the club should be looking to reward the player with the club captaincy - rather than refusing to meet his wage demands.
"For me he's a future Arsenal captain. I know he loves the club. It's difficult for me to comment on because I'm not there but I do know he's a great player – if it was me I know I would want to keep him around.
"He's a great guy to have around. He's been at the club so long and knows it inside out. If you look at what he's done for the club too.
"We went into the first team in the same year. He came from Cardiff and I came from the youth team. We automatically clicked because we were both young and new to that sort of environment."
With Manchester United, Juventus, AC Milan all linked with shock moves with the Wales international, former playmaker Paul Merson, now a pundit feels it would be a 'typical Arsenal' move to allow a player of his magnitude departs without compensation.
"But giving a player £200,000-a-week is going to be a lot less than buying a £40million player and giving him £130,000-a-week. It's typical Arsenal, isn't it?"
"How can they let the contract of a quality player like that run down? They’ve done it too many times now."