The Liverpool and Wales midfielder has been subject to interest from a number of Premier League clubs, including Allen's former side Swansea and Liverpool's fierce rivals Manchester United.
However, it is Stoke City who look most likely to sign the 26-year-old as Liverpool have accepted their offer of £13m.
Liverpool boss Jurgen Klopp still believes that Allen is a good player, but Liverpool may be forced to sell as the midfielder's contract runs out at the of the 2016-17 season and they will not want to risk letting Allen go for free.
"I feel good about Joe," Klopp said. "I like the guy and I really think he is a wonderful football player. I knew this before the European Championship, I saw it during the Euros and I know it now".