Ronny Deila's side are currently six points clear at the top of the Scottish Premiership.
The 32-year-old joined the Hoops in October, and while being without a club since the summer meant that Ronny Deila had to take things slowly with the former West Ham and Chelsea striker, he has now made five appearances for the team, and scored during the Scottish Cup victory over Stranraer earlier this month.
And while there are several months of the season still to go, Cole is looking ahead and hoping that his side are lifting plenty of silverware come the end of the campaign.
"Winning a Treble with Celtic would absolutely be up there with any achievement I have had in the game – it is a huge thing," Cole told the Evening Times.
"I would love to really weave my name into the fabric of this club. It is such a big club with a reputation all over Europe."
Cole's goal against Stranraer helped the Bhoys to a 3-0 win - with Leigh Griffiths bagging a brace - which saw them book their place in the fifth round. And they will go into that game as heavy favourites to progress to the quarter-finals as they are due to come up against Lowland League side East Kilbride.
They are also in a strong position in the Scottish League Cup. Victories against Raith and Hearts has seen Deila's men set up a semi-final clash with Ross County.
But it is arguably in the Scottish Premiership that the Hoops stand the strongest chance of securing silverware. They currently sit six points clear of nearest rivals Aberdeen, leaving them well on course to secure their 47th league title.