Fletcher, who made the switch from Wolves to Wearside for a fee of £12 million this summer, has scored five of Sunderland's six league goals, the other an own goal by Newcastle's Demba Ba in last weekend's Wear-Tyne derby.
"If you look at the records so far, with the goals he's scored, obviously he's going to be a danger," Pulis said of the in-form Fletcher. "We might have tried (to sign Fletcher) but we've tried with a lot of players."
He went on: "But they've got good midfield players. If you look at Adam Johnson, (Sebastian) Larsson's very good off set plays. (James) McClean is good on the other side. (Stephane) Sessegnon can win games. They've got experience at the back so they're a decent side."
Stoke have only earned themselves eight points from their opening eight Premier League games this season, something which has disappointed Pulis despite the calibre of their opposition.
The Potters have faced Arsenal, Manchester City, Chelsea, Liverpool and Manchester United in a tough start to their campaign but now face a less daunting sequence of fixtures where they are scheduled to play Sunderland, Norwich, QPR, West Ham and Fulham.
Sunderland have also picked up eight points from their opening fixtures but still have a game in hand thanks to the postponement of their match against Reading.
Pulis thinks Martin O'Neill's Sunderland are similar to his side as they need something to kick-start their season, with both sides only having one Premier League win to show so far.
"They've got some very good players and he (O'Neill) has got the basis of a very decent squad there," Pulis said. "They're a bit like us. They need a couple of results and a couple of breaks just to get themselves moving. I see them as being, they are and will be, a very competitive Premier League side.
"We've enjoyed the season so far. It's been a tough start. We've played five of the first eight games at home and two of our home games have been against Man City and Arsenal so it's been a very difficult start for us."
Source: PA
Source: PA