The Wales international's future is uncertain at the north London side given the versatile midfielder hasn't committed to a new contract at Arsenal.
However, with both parties feeling as if they were close to an agreement, Arsenal made the shock decision to withdraw their offer to Ramsey.
Arsenal handed Mesut Ozil a contract worth a reported £350,000 a week back in February to make the former Germany global the highest paid player in their history. Premier League rivals Manchester United, Chelsea and Liverpool and top Serie A clubs are all interested in signing the Welshman.
United, though, face competition from Liverpool with Jurgen Klopp also a big fan of the 27-year-old who scored one of the goal's of the season so far against Fulham before the worldwide break.
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But Wenger, who attempted to persuade Ramsey to sign a new deal before he left Arsenal at the end of last season, said he did not feel the 27-year-old would definitely leave.
The Welshman is on global duty and he said, "Will I stay for the rest of the season? That's all I am concentrating on and giving my best for Arsenal".
"Everything has been going great with the club". That makes it hard to win it but we've come on leaps and bounds over the last couple of years and we're in a position now where we can really challenge. He further said, "So I just have to carry on playing my football and do my best for Arsenal this season". Of course, yeah. I am contracted to Arsenal.
The Wales worldwide, who scored a stunning back-heel effort in Arsenal's 5-1 win at Fulham on Sunday, has scored 59 goals in 338 appearances for Arsenal since joining from Cardiff in 2008.