The Daily Mail says the 55-year-old has done an excellent job after guiding Stoke into the Barclays Premier League in 2008. Since then, Pulis has taken the club to a Wembley FA Cup final and into Europe.
He has never been relegated as a manager, but has come under massive pressure to alter the team's style of play this season.
Pulis will not resign but Stoke are preparing to offer a compromise agreement as they consider their options in the coming days.
The manager, who led the club to 13th place in the Premier League this campaign - six points clear of safety - fears that he is being pushed out of the door.