The Wales international’s future at the north London side has been a source of persistent speculation over the past few months.
Ramsey has been unable to agree to a contract despite entering into protracted negotiations with the Gunners earlier this year.
Chelsea FC and Manchester United have both been linked with a potential swoop to sign the Arsenal midfielder over the past few months.
The Blues could be an attractive proposition to Ramsey given the Welsh star could remain in London without uprooting his family.
However, Maurizio Sarri has a wealth of midfielders to choose from following the arrival of Jorginho and Matteo Kovacic in the summer.
Furthermore, January signing Ross Barkley has come into his own over the past few weeks following his recovery from an injury.
The England international has already made nine appearances in the current campaign to highlight his importance to Sarri.
Former Arsenal star Wright believes Chelsea FC would struggle to find a place for Ramsey given Barkley’s resurgence.
“Chelsea have Barkley and Loftus-Cheek,” Wright told Sky Sports.
“Barkley has had the injury. He has come back and looks pretty sharp. His confidence is starting come back to him.
“Am I going to bring Ramsey in and halt that progress? Barkley will score goals when in form.”
Ramsey has established himself as an important member of the Arsenal team since Unai Emery’s appointment in the summer.
The Welsh star has started six games and has made one appearance from the bench to help Arsenal secure fifth spot in the table ahead of their trip to Fulham on Sunday.
Arsenal managed to see off competition from Manchester United to sign Ramsey after both Arsene Wenger and Sir Alex Ferguson met the Welsh talent.
Barkley, meanwhile, moved to Chelsea FC from Everton in a cut price £15m deal in the January transfer window under Antonio Conte’s management.
The England star was previously linked with top clubs such as Manchester City and Manchester United but Barkley has struggled in recent seasons.
Barkley is still waiting to open his Chelsea FC account despite having made 13 appearances in all competitions so far.
The Merseyside-born playmaker netted 27 times in 197 games for his boyhood club Everton, producing his best form under ex-Toffees boss Roberto Martinez.
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