Wilson sustained a fractured left fibula in last Saturday's 0-0 Premier League draw with Sunderland at the Britannia Stadium as he made a challenge on Black Cats striker Steven Fletcher, and had to be carried off on a stretcher.
Stoke this week indicated the 25-year-old was facing up to three months on the sidelines, but Pulis is hopeful it will not take that full duration for Wilson to return to fitness.
Speaking this afternoon at a press conference ahead of Saturday's away clash with Norwich, Pulis said: "It's three months at least I think.
"But we are hoping, with the medical staff we have got and the way they overachieve in lots of respects, it might even be quicker than that - fingers crossed.
"We have Wilko (Andy Wilkinson) who can slot in (at left-back), but we are disappointed with what has happened to Marc. I think he has probably been our most consistent player this year - he is a very underrated lad and we will miss him because he has great quality."