United currently sit five points clear at the top of the table but City have the chance to slice that lead to two points when they visit QPR on Tuesday, with the Red Devils playing a day later at home to Southampton.
Roberto Mancini's men will be encouraged by last term, when United let their lead slip away in the final weeks of the season, allowing City to clinch the trophy on the final day of the campaign.
United defender Patrice Evra admitted last week that part of his side's problem last season was a preoccupation with their neighbours which made them lose focus, though insisted they will have no such problem this year.
However, rival left-back Clichy is hoping City can get under their skin once again.
He told The Times: "I was surprised he (Evra) said that because a club like them know how to win titles in this league.
"It was good to hear because it meant we are progressing and that any team, even if it's United, can get a bit nervous when they feel the pressure of someone behind them, breathing down their neck and saying, 'I'm going to be right behind you if you make a mistake'.
"It's probably a bit different for them because it's two clubs from the same city, whereas Arsenal and Chelsea (their main rivals in the past) are from London.
"I'm not saying United should be scared, but they should be a bit worried because we will be there until the end of this season again.
"We expected United to come back strongly. It will have hurt them for us to win the title like we did with the last kick of the final game, but we are confident and we remember what happened last time."
Clichy feels the arrival of Robin van Persie at Manchester United from Arsenal in the summer has made a massive difference to their season.
The Dutchman has already scored 22 goals in 28 appearances for United and Clichy added: "A player like Robin is a player that any manager would like to have.
"I'm sure the boss is disappointed about missing out on him when you see the season he is having so far."
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