The 21-year-old forward has struggled to get first team chances at Arsenal since he made his debut in the League Cup in October 2006.
Simpson had a loan spell at Millwall and then spent six months with West Bromwich Albion when they were in the Premier League in 2009, scoring two goals in 13 appearances.
It was last season on loan at Queens Park Rangers where the forward really impressed, scoring 12 goals in 39 appearances and showing he can find the net at Championship level.
Simpson sits below the likes of Robin van Persie, Marouane Chamakh, Nicklas Bendtner and Carlos Vela in the striking pecking order at Arsenal, and it looks like his Gunners career could be coming to an end.
His agent Uben Gray has spoken to Sky Sports and told them that Leeds United, Hull City, Crystal Palace and QPR have all been in touch with Arsenal and are now in talks with the striker.
It is believed that a fee of around £1.2 million would be enough to get Simpson's signature and Yorkshire sides Leeds and Hull are leading the chase.
"I can confirm a couple of clubs have agreed a deal with Arsenal and we are now in talks with them," said Gray.