Charlie Adam had been planning to stay at Anfield this season
Stoke City manager Pulis wants the former Blackpool midfielder to bolster his options at the Britannia Stadium.
Pulis has moved for Adam, who appears surplus to requirements under new Anfield manager Brendan Rodgers, after considering alternative deals for Spurs' Tom Huddlestone and Blackburn Rovers' Steven N'Zonzi. He faces opposition from Fulham and Everton, who have both made tentative enquiries for the 26-year-old and Turkish club Fenerbahce is are also another potential destination.