Owen has played only 10 times since January 29 2011, so Stoke are weighing up the 32-year-old's fitness and wage demands before signing him.
Pulis revealed: "We're monitoring him, so it's a case of waiting to see what happens. We tried to find out what he was doing a couple of years ago. But nothing came of it.
"Everyone knows Michael's pedigree and the fact he has performed with such distinction at the highest level, for club and country."