Ramsey earns around £90,000-a-week at the Emirates but he expects a significant increase on that to sign a new long-term deal.
New head coach Unai Emery is keen to keep Ramsey at the club, and possibly appoint him captain in succession to the retired Per Mertesacker.
Ramsey has been at Arsenal for nearly a decade after joining from the Bluebirds in June 2008.
At the age of 68 and with three Premier League titles already to his name, Wenger could have been forgiven if he wanted to retire.
Aaron Ramsey is Arsenal's current longest serving player with the Welshman close to completing a decade with the North London Club.
However, he's yet to accept Arsenal's offer and the club do not want to lose him on a free next summer.
This season he won Arsenal's Player of the Season for a second time scoring 11 goals and picking up 9 assists, repeating his heroics from the 2013/2014 season. The 27-year-old has been with Arsenal since joining from Cardiff back in 2008. Chelsea are reportedly one of them, as are Juventus.
There are claims the French giants have made the midfielder a massive financial offer to stay in Paris, but the youngster has got his mind set on England, where he thinks he can develop further.
Emery certainly has the tools to succeed at Arsenal.
Emery is planning on making Ramsey "central to his plans" for next season, according to Sky Sports News.