The England international's two-year spell at the London outfit has been trophy-laden thus far, with the center back counting the FA Cup, Champions League and Europa League among his growing list of medals.
But the 28-year-old has yet to collect the domestic league title, and is eager to join the likes of John Terry, Frank Lampard and Petr Cech in tasting top-flight success.
"It's one of the biggest trophies you can win and I'm sure the lads who have won it before would say the same thing," Cahill told reporters.
"They're just as hungry as me to do it again. As I've never won it, it would be a great achievement in my career and one I'm striving to do."
Chelsea's hopes of title success were boosted with a comprehensive 3-1 victory over reigning champion Manchester United at Stamford Bridge on Sunday, extending manager Jose Mourinho's unbeaten home record in the Premier League over his two spells at the club.
Cahill believes the Blues can achieve the consistency required to pip the likes of Arsenal and Manchester City in the title race.
He added: "It is an incredible record and one day it will come to an end, but hopefully not too soon. We have confidence whenever we play at home, which we should have, and always manage to get results here.
"Hopefully that will continue for the rest of the season, but the main thing for us is consistency, to keep performing every week. The lads have got the drive to do that right now and things are going well."