New manager, Unai Emery, however, views Ramsey as central to his plans for next season as he plans to build a team around the Welshman.
However, Ramsey is asking for a significant increase of his current £110,000-a-week wage.
The Daily Mail says the 17-year-old midfielder is poised to sign a three-year deal with the Gunners after rejecting a professional contract with PSG. He will be sold if he refuses to extend his contract.
Ramsey has been at Arsenal for nearly a decade after joining from the Bluebirds in June 2008.
The former Valencia boss has taken charge of seven clubs over the last 14 years. Since then Ramsey has played 331 senior games for the Gunners in all competitions, scoring 59 goals.
The midfielder and his advisor have been in talks over a new deal for several weeks and an offer has now been made.
Arsenal have reportedly inserted a break clause in Unai Emery's contract to avoid a repeat of the situation with Manchester United and David Moyes (via The Times).
Emery is planning on making Ramsey "central to his plans" for next season, according to Sky Sports News.
There are comparisons between Adli and a young Nicolas Anelka, and talkSPORT claim that Emery could make the young striker his first signing. In the end, Arsenal fans must be hoping their star midfielder stays put with them for the next five years.