The Blues maintained their pursuit of leaders Arsenal with an Eden Hazard-inspired 4-3 victory at bottom-of-the-table Sunderland on Wednesday evening, and head for Stoke on Saturday needing to repeat the feat if they are to maintain pace with the Gunners.
Many members of the current team have no experience of winning the title, which the club did in 2004-05, 2005-06 and 2009-10.
However, Cahill is confident the manager who claimed those first two successes and the senior players who formed the backbone of his team can school a new generation in how to go all the way.
He told the club's official website, www.chelseafc.com: "It's very tight at the top. All we can do is keep trying to win.
"We did that on Sunday [against Southampton] and on Wednesday we went away from home to a team that is fighting and made it very hard for us, but again we got the win.
"Jose's experience will definitely help us this season. I've won cup competitions but I've never won the league, and it's one of my goals that I'm aiming to achieve.
"We have got players that have won the league a few times. They have got a lot of experience to give the younger players, like Eden, and we can all take confidence from them."
Hazard turned in an individual display at the Stadium of Light which left both Mourinho and opposite number Gus Poyet saluting his contribution.
He made Frank Lampard's 17th-minute equaliser and then scored his side's second and third goals, although it was Sunderland defender Phil Bardsley who effectively sealed the victory six minutes from time when he turned substitute Demba Ba's cross into his own net.
Mourinho will hope for more of the same from the 22-year-old Belgian as he attempts to bring the league trophy back to Stamford Bridge.
The man himself knows that will be far from easy, but he believes there is enough talent within the squad to push Arsene Wenger's men all the way.
Hazard said: "Arsenal is top and now we need to take three points every game.
"There are big teams with us and it is difficult but we have a very good team - a young team but very good team - and we will see after December and January."
If the Blues are to succeed, they will need to defend significantly better than they did on Wearside, where all three of Sunderland's goals came from set-pieces, although Cahill is not unduly concerned.
The 27-year-old said: "If you take away the set-pieces - which we know is a huge part of the game - we limited Sunderland to few chances and defended well.
"It was unlike us because we have done all right with set-pieces this season."