The 55-year-old met chairman Peter Coates following a difficult end to the 2012-13 season that saw the Potters flirt with relegation.
Although Pulis ultimately led his side to safety with two wins from their final five games, Stoke finished the campaign with just 42 points - a Premier League low for the club.
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And in a statement to Goal, the club confirmed that an announcement would be made by "close of play" on Tuesday.
Michael Owen, who played the final match of his career on Sunday for the Potters, tweeted: "Just heard that Tony Pulis has left Stoke. No denying he did a great job getting them to The Premier League and keeping them there."
Pulis has spent seven years at the Britannia Stadium after joining the club for his second spell in 2006. During this time he led the Potters to an FA Cup final in 2010-11 and subsequent Europa League campaign in 2011-12.
However, a dismal set of results that yielded just three victories in 2013 saw a portion of the fanbase become disenchanted with Pulis' style, particularly considering the considerable sums of money spent by the club in recent years.