Gunners will let youngster leave if the 'deal is right'...
The 21-year-old graduated out of the Gunners' youth academy, and has had loan spells at Milwall, West Bromwich Albion and recently Queens Park Rangers.
However, the youngster has not been able to carve out a place in Arsenal's first-team, and has consequently been told that he can leave if the right offer arrives.
"Jay has had discussions with Arsene Wenger and Arsenal," Gray told Sky Sports.
"Everyone at the club only has good things to say about Jay, including Arsene, but they appreciate he needs to be playing first-team football.
"And so they are ready to let him leave, but only if the deal is right for all parties."
It is believed that Blackpool, Fulham and Hull City are among the clubs chasing Simpson's services.
Simpson scored 13 goals in 42 Championship and cup games last season for QPR, who endured five managerial changes during the course of the campaign. He has made three first-team appearances for Arsenal (including two as a substitute), all in 2008-09, and scored two goals - both of them in a League Cup tie against Wigan Athletic in his first start for the club.