Previous results give little indication of how Sunday's match will pan out, with Stoke winning the home Barclays Premier League game and drawing at Liverpool while Kenny Dalglish's side edged their Carling Cup fourth-round meeting at the Britannia Stadium.
Stoke went all the way in the FA Cup last year, thrashing Bolton 5-0 in the semi-finals at Wembley before losing narrowly to Manchester City in the final.
But Pulis has no doubt as to the size of the task in front of them against Liverpool, particularly with the game being at Anfield, where Stoke have not won since 1959.
"We know how difficult it's going to be," said the Welshman. "It's a very tough game for us. Liverpool are a very good side, especially at home.
"We've watched them the last few weeks and they were desperately unlucky to lose to Arsenal, that game should have been over in the first 45 minutes.
"I went and watched the derby on Tuesday night and I thought they were outstanding.
"This will be the fourth time we've played them this season and they've always been tight games and good games. They're obviously favourites and rightly so but we'll do our best, as we always do.
"It gives us heart that we've played them three times and given them a good run for their money on three occasions, and that will be the theme this week.
"If we can just raise the bar a little bit again then, if things go for us, we might get the result everybody in Stoke-on Trent wants."
Liverpool have been unusually vulnerable at home this season, but they were in impressive form in beating Everton 3-0 on Tuesday.
Stoke are guaranteed great support, though, after selling out their allocation of tickets, which were available for only £20 after being subsidised by owner Peter Coates.
Pulis said: "It's a great gesture by Peter and the Coates family. It just shows the togetherness that we've got at the football club from boardroom level through to the people on the street.
"They understand the area, Peter's been here for 74 years and he understands that sometimes you have to do deals like this to help the supporters.
"They'll be fantastic. We took nearly 6,000 to Derby and that helped us immensely so to take 6,000 to Anfield will make it a fantastic atmosphere."
The Potters will be without striker Ricardo Fuller, who serves the first game of a three-match ban following his red card at Chelsea last weekend, but Pulis has no fresh injury worries and will bring in former Liverpool striker Peter Crouch, who was rested at Stamford Bridge.
"I thought it was right to give him a rest at Chelsea," said the Stoke boss. "His stats have been unbelievable and I wanted him fit for this week, and obviously the Liverpool game is the big game."
Pulis must again decide whether to recall another former Red, right winger Jermaine Pennant, who has been usurped this season by Ryan Shotton, a player who began his career in the Stoke youth team.
Pulis hailed the progress made by 23-year-old Shotton, saying: "I've taken some stick because I've left Pennant out and played Shotton but I've been really pleased with Ryan. Having him and Wilko (Andy Wilkinson), two local lads, on the same side of the pitch is brilliant.
"He's got loads to work on and improve on but he's really enjoyed and relished the games, and he's played in some tough games and done smashing.
"It's great that we've got players who have come through the academy. It helps everything we're trying to do at the football club."