The Republic of Ireland winger was due to move to Fratton Park along with David Kitson as part of the deal that saw Marc Wilson move to the Britannia Stadium.
The move was not completed before 5pm last Thursday, but with the international break he has not missed any games for Portsmouth. He could join them as early as Wednesday.
"We're disappointed that this transfer hasn't gone through. The aim now is to ensure we arrive at the same point for both clubs and the player who had made up his mind up to join Portsmouth," said Tony Scholes, chief executive of Stoke.
"That will probably take the form of a loan move until the end of the year and then Liam would finalise his permanent move to Fratton Park in the January window."
Portsmouth also expect to sign the right-back Kyle Naughton on loan from Tottenham Hotspur.