The 32-year-old striker was released by Manchester United in May and there were rumours that he would retire after managing to play just over 50 games in three years at Old Trafford.
But the former England international rubbished reports that he would hang up his boots early, having previously said that he intends to remain in the Premier League.
“We tried to find out what he was doing a couple of years ago but nothing came of it – and it was a couple of years ago,” Pulis told The Sentinel.
“Everyone knows Michael’s pedigree and the fact he has performed with such distinction at the highest level for club and country.
“We are monitoring him, but along with about 400 other players to be honest, so it’s a case of waiting to see what happens.”
Should Owen move to the Britannia Stadium he would reunite with former England teammate Peter Crouch who joined last summer from Tottenham for £10 million.
The duo played together at the 2006 World Cup in Germany and it looks as if they’ll be given the chance to rekindle their partnership at Stoke.
His arrival would certainly represent a shift away from the reputation the Potters have garnered as a long ball team during their four-years in the Premier League.