Ramsey scored in Arsenal's 5-1 win over Fulham earlier this month and has made over 300 appearances for Arsenal in all competitions.
Ramsey has already insisted he has no plans to leave Arsenal in January, but did admit he thought he had agreed a new deal before the Gunners called a halt to talks.
Aaron Ramsey's camp have refused to rule out a move to Manchester United at the end of the season.
Ramsey will be free to sign a pre-contract agreement with foreign clubs in January and has said in the past he's tempted by a move overseas but the midfielder will also have plenty of options if he decides to remain in England.
Wenger feels the 27-year-old is in a strong position at Arsenal despite the club withdrawing a contract offer.
Ramsey, who turns 29 in December, may be tempted by such a long-term deal, but would need further convincing to turn down the advances of top clubs like Chelsea.
The report details that Ramsey could command a £15million signing-on fee, while the likes of Liverpool, Chelsea and Manchester United are all monitoring his situation.
Ramsey would likely demand huge wages were he to join United.