The Potters held Arsenal to a 1-1 draw on Saturday, while Everton scored four goals for the third game in a row by thrashing Fulham at Goodison Park.
But Cahill expects a totally different game, telling the club's official website: “I think it's hard to look forward to Stoke because physically they're very demanding and tactically, with their long throws and their set plays, it can be quite a grind.
"There's a bit of a similarity with the group of players they've got and the closeness to Everton. And, for us, if we go to a place like that even at 90 percent, it's not going to be enough. We really need to make sure that we stop them physically and then hopefully we play enough football to win the game."
Cahill understands the threat that Stoke can pose and believes their manager is to thank for their continued Premier League status.
"Tony Pulis has done a great job with that team and obviously the players that they've got work really well together,” he said.
Everton currently sit two points above their Merseyside rivals Liverpool, and despite the heartache of their FA Cup semi-final defeat Cahill is pleased that their hard work is paying dividends in the league.
"I think after the heartache of the FA Cup it was just right that we focused on the league," said the 32-year-old midfielder.
"To finish above Liverpool we have to be really determined and try to get the right results. We have to be on song because it's such a massive thing to finish above Liverpool and I think for the fans it would be a just reward for what we've been through this season."
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