The People says Pulis is on red alert as the Canadian starlet refuses to sign a new deal.
The 21-year-old's contract with Rovers runs out in June, and the Potters are prepared to offer more money for Hoilett in January than rivals Tottenham and Newcastle United who are also in the hunt.
Pulis considers Hoilett a perfect addition to his improving squad.
He can play on the left wing or the right and even through the middle if Stoke want to mix it up. Pulis has ready cash to strengthen and could go over £10million in an effort to land Hoilett, who is valued even higher by Rovers and their Indian owners.