Sheepshanks told the club site: "After much soul-searching Tony has decided that he does not wish to leave Hibernian for the time being.
"Permission was granted by Hibs for us to speak to Tony earlier this week and I had a long, friendly discussion with him about the vacancy.
"However, at this time and despite Tony's great affection for the club, which he emphasised during our talks, he feels he is not ready to return to Portman Road so soon and we must respect his decision."
Sheepshanks and Chief Executive Derek Bowden are understood to be in London conducting interviews in the search for a new manager.