As it currently stands, the 27-year-old Welshman will become a free agent at the end of the season when his current contract at the Emirates expires. There have not yet been any agreements over a contract extension.
Arsenal are reportedly confident that the player will put pen to paper, but it is likely that Ramsey will follow teammate Mesut Ozil's example and hold out until January when he is free to listen to offers from other clubs in Europe.
Ramsey's teammate Ozil utilized a similar tactic last season, earning himself a reported £300,000-a-week contract as the Gunners desperately tried to keep hold of their midfield star.
Manager Unai Emery is said to want Ramsey to stay and will urge the club to bring negotiations to a successful conclusion.
The offer to Ramsey will reportedly be on par with what Ozil agreed to, avoiding the prospect of the player agreeing to sign for a club on continental Europe or joining another club in England on a free transfer next June.
Having joined Arsenal back in 2008, he has gone on to make 332 appearances in all competitions and score 58 goals.
The Welsh midfielder made his senior international debut in 2008 and has gone on to earn 53 caps to date, netting 13 times.