The Potters go into the Premier League clash at the Liberty Stadium off the back of two impressive results over the past few days, a 2-1 come-from-behind victory against Turkish side Besiktas in the Europa League on Thursday and last weekend's 1-1 draw with Manchester United, both at home.
A fortnight earlier, the Staffordshire outfit had overcome Liverpool 1-0 at the Britannia Stadium and then held Dynamo Kiev to a 1-1 draw in Ukraine in their Europa League Group E opener, only to be hammered 4-0 at Sunderland on the Sunday.
It was their first - and to this point sole - defeat of the campaign, and Pulis is keen to avoid a repeat against the Swans.
"The big challenge is raising your game for matches in a week, which is what we need to do at Swansea after the excellent results against Manchester United and Besiktas," Pulis told the club's official website.
"We had a similar sequence in the lead-up to Sunderland when we beat Liverpool and then drew out in the Ukraine against Dynamo Kiev, so that is a sobering reminder of what can happen if we're not right on it in this instance.
"I'm told the record books show that sides who have successful Europa League campaigns find that their league form drops off as a result, so it will be very interesting to see what happens, but we are very mindful of that."
Pulis is also well aware of the threat posed by newly-promoted Swansea, the Premier League's first Welsh club who recorded their maiden victory in the division in their last home game with a 3-0 triumph against West Brom.
"Swansea have done fantastically as a football club over the past five or six years - not just since (their manager) Brendan Rodgers came in, but prior to that as well," Pulis said.
"They have built a smashing football club there with an almost brand new stadium which has a fantastic atmosphere.
"I've watched them twice this year and they are a very, very good side. They pass the ball around well and they have good players.
"He (Rodgers) has put a belief into them that they can win matches.
"You only have to look at the result against West Brom to see what they can do, so it is going to be a massive game for us and a tough one."
As a proud Welshman, Pulis wants to see Swansea flourish this term - aside from Sunday and when they visit the Britannia Stadium, of course.
"I hope Swansea do well all season apart from in the two games where they play Stoke," Pulis said.
"I'd love Newport County to be promoted from the conference, Cardiff to get promoted out of the Championship and Swansea to stay in the Premier League. That would be a great year for Welsh football."
Source: Team Talk
Source: Team Talk