Spurs moved to within two points of Roberto Mancini's side after a sensational 3-3 draw with rivals Arsenal at White Hart Lane on Wednesday night.
While Crouch appreciates his side still have to pick up points against West Brom, Chelsea and Blackpool before facing the club they beat to fourth last season thanks to his goal in a 1-0 win at Eastlands, the forward hopes Mancini will set his side up to play for a victory.
"They're at home," he said. "If I was the manager I'd come out and play, but that's up to them.
"I hope they do because hopefully it's an entertaining game of football, everyone will be watching it and it's like a cup final in many ways."
The England international also believes that while the money spent at Eastlands has built a weight of expectation on City, Spurs is also under pressure after reaching the quarterfinals of the Champions League in their debut season in the competition.
He added: "They're probably under more pressure than we are but that doesn't make us have any less desire.
"We have got probably a bit more freedom but there is pressure on us because we've loved every minute of the Champions League this year, it's been fantastic and it's what we want again next season.
"We've proved we can play against the best and that's where we want to be."
Crouch was denied a goal against Arsenal as Wojciech Szczesny tipped his headed effort over the bar but was pleased to have taken part in the spectacle, even if Spurs were unable to secure what he believes would have been a deserved victory after coming from 3-1 behind.
"I'm gutted I missed out on watching it really, it was a great game of football," Crouch said.
"I thought in the end only one team was going to win it, obviously they were dangerous on the break but I thought in the second half we were fantastic and deserved to win it.
"You could see both team were all out going for the win. It's a little bit frustrating, but we've still closed the gap, it's two points now on Man City with the same games played, so it might rest on going up there again."
The draw marked another game in which Tottenham have secured a point against one of the league's perceived bigger clubs, while Crouch was left to rue his side's inability to beat teams at the other end of the table.
"Against the top teams we've been magnificent for a couple of years now," he added. "If you've got any aspirations of winning the league you have to make sure you win games against lower teams in the division and we've slipped up a few times this season.
"They're the most frustrating points to have dropped, but on the big occasion we're fantastic."
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