Antonio Conte’s side have won each of their last 11 league games, and are on the brink of setting an outright club top-flight record if they win Monday’s match at Stamford Bridge.
Defender Cahill insists the players have not spoken about the statistic, but they are hungry to put their names in the history books.
“It’s not something we speak about on a daily basis,” he told Soccer Special.
“In fact, I haven’t heard any of the lads speak about it, but we know about it and I’m aware of it. Of course you want to be involved in teams that break records and you want to be involved in teams that do well.
“We’re aware of it and the Boxing Day game is a chance for us to do that, which should add extra incentive. We want the three points badly and we want the record.
“I’ll speak for myself, I want the record. Why would you not? There’s three points and a record to go for.
“If you’re asking me if I’m going to be motivated for that game, I think we’re all in the same boat.”
The winning run has taken Chelsea six points clear at the top of the table at Christmas as they bid to regain the Premier League title they won in 2014-15.
After a disappointing campaign last season, which left them outside the European places in 10th, Cahill insists their improvement under Conte is down to a variety of factors.
“It’s fantastic,” he added.
“The mood in the camp at the minute, everyone’s spirits are high. Everyone will tell you that playing in a winning team is easier. The run that we’re on is brilliant so I hope it continues. We’re full of confidence.
“What’s going right is a number of things. Obviously people will touch on the change in formation, but there’s the way we’ve adapted to that formation and the players we have in the team, ultimately.
“A lot was made of last year and rightly so. We had individuals, the majority, underperforming compared to the levels they usually set.
“This season we are hitting the levels we should be setting. I’d be lying if I said I thought we’d be sitting pretty at the top of the table, but I certainly would have expected to be up there competing.
“We’re in a good place.”
Cahill is now playing on the left of a back three, rather than the right of two centre-backs, following Conte’s decision to switch from 4-3-3 to 3-4-3 earlier this season.
Many people have pointed to the tactical change as the reason for the team’s improved results, but Cahill says the hard work of the players has been just as important.
“The manager knows his formation inside out and we have worked very hard on the training pitch to adapt to that formation,” he said.
“People talk about the formation, but I think it’s the way we’re playing that formation – and that comes a lot from the manager and his experience with this formation and ultimately the lads taking it on board and going out and delivering it.
“It’s a number of things that have given us success, it’s not just all of a sudden ‘we’ll play this formation, off you go…’
“It doesn’t work like that. You have to put a lot of work in on the training ground.”