The Wales international has entered his final 12 months of his current deal with the north London outfit to fuel transfer speculation surrounding his future at Arsenal.
Ramsey could become a free agent at the end of the 2018-19 Premier League season unless there is a fresh development in negotiations.
Arsenal have reportedly taken their contract offer off the table after Ramsey failed to agree terms with the Gunners despite nearing the end of his current deal.
The former Cardiff City man has been linked with a potential move to Chelsea FC and Manchester United in recent weeks, as well as Serie A giants Juventus.
Ramsey has started six of Arsenal’s seven games in the Premier League this season to underline his importance to Arsene Wenger’s replacement Unai Emery.
The Welsh star has become a key member of the north London side’s midfield over the past three or four seasons under Emery’s predecessor.
Former Chelsea FC striker Sutton believes Arsenal have made a mistake deciding to pull the plug on negotiations with the 27-year-old.
“I don’t understand why Arsenal withdrew the contract offer,” Sutton told BBC Radio 5 Live.
“He is one of their better midfielders. They should have tied him down.”
Arsenal set a dangerous precedent when the Gunners opted to hand Mesut Ozil a contract worth in the region of £350,000 a week at The Emirates.
The Gunners made the Germany international the best paid player in their long history despite the World Cup winner’s patchy form.
Ramsey has started more games than Ozil under Emery, although the German playmaker has netted two goals but the versatile midfielder is yet to open his account this term.
The Welsh star moved to Arsenal from Cardiff City in 2006 after Ramsey opted to move to the Gunners to work with Wenger instead of a switch to Manchester United.
Ramsey has won three FA Cup titles during his 12-year spell at the The Emirates but the Welsh star has never won the Premier League title.
The Arsenal star has scored 58 goals in 336 games in all competitions during his long spell at the north London side.
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