The 34-year-old, a free agent after leaving Aston Villa, turned down offers earlier in the summer but believes he is now edging closer to a playing return.
Heskey, who is open to a move abroad but would prefer to remain in England, is still able to sign for a club even though the transfer window has closed.
"I feel as fit and hungry as I have done in a long time and have been training everyday throughout the summer," he told journalists.
"As has been reported I did receive a number of offers during the transfer window but didn't feel like any of them were the right opportunity for me at that time.
"I'm now looking forward to hopefully securing a new club over the coming days."
Journalists in the media understand that Stoke, Norwich and Spanish side Espanyol have made tentative enquiries about Heskey, who has 62 England caps and played 29 times for Villa last season.
Reports have also linked Heskey with former club Liverpool, whose failure to land a replacement after sending Andy Carroll out on loan has left them desperately short of strikers and now looking for free agents to potentially sign.