The former Arsenal and Hull City forward had travelled to Turkey for talks over the weekend, but he has opted against signing the deal.
Simpson, who has interest from a number of clubs around Europe, has now returned to England to consider his options.
"The interest in Jay is high," his agent Leon Callander told Sky Sports.
"He does like the idea of playing abroad, and that is why we had the talks in Turkey, but things were not quite right.
"We will be assessing the options over the coming days and see what is best for him."