Kieran Tierney had not started primary school the last time Celtic won a Treble.

Not that it went over his head.

Born into a family of Celtic fans, the 19-year-old grew up surrounded by the paraphernalia of that era – and the stories of Henrik Larsson, Chris Sutton and Stiliyan Petrov that went with it.

This season Tierney has the chance to write his own name into the script and while the Scotland internationalist is wary of taking too much for granted, he is nevertheless tickled at the chance to be a part of something that could prove to be an historic achievement.

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“I have to be honest and say that I don’t really remember the last time that Celtic won a Treble as I was quite young,” he smiled. “But at home we had all the DVDs and I always knew about the games and what had happened.

“It feels like a privilege to be in a position that we are now where we have the chance to achieve something like that. But we don’t want to get too far ahead of ourselves. I think the gaffer has made it clear that it is always about who is up next and if we can focus on that then the rest should take care of itself.”

Celtic are 20 consecutive league games without defeat – and counting. So far only Inverness have taken points off them in the league while the Parkhead side are unbeaten in both Cup competitions.

St Mirren await in the quarter-final of the William Hill Scottish Cup but it is difficult to see just any other domestic team being able to stop the momentum that Celtic have established this season.

Going through the campaign as invincibles would be exceptional achievement but the mantra of his manager has stuck firmly with Tierney.

“I just think it is great to be in this position,” he said. “We don’t really think about the lead at the top of the table or anything else. It sounds a bit boring but we really do just think about the next game and take it from there.

“There is still quite a lot of football to be played this season. It is nice to have the lead and it is nice to have won the League Cup already but there is an awful lot of games on the horizon. The good thing just now is that we are getting a chance to take a breather and work on things at Lennoxtown because we don’t have games during the week and then the weekend.

“The manager wants us to not just keep the standard there but to improve it and that is what we aim to do. I just feel lucky to be a part of it. The dream is to win a Treble, it is the same dream we have that every Celtic fan has but it is important we go about trying to achieve that the right way.”

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Moussa Dembele netted his 27th goal of the season at the weekend as Motherwell were brushed aside at Celtic Park, and the Frenchman has been watched by clubs all over Europe this season.

Chelsea noted their interest in the 19-year-old during the January transfer window while Bayern Munich and Real Madrid are the latest to be credited with charting the progression of Dembele.

The striker has repeatedly maintained that he is in no rush to quit Glasgow and Tierney was delighted to see the January window close with the Celtic squad still intact.

“He has been brilliant for us and everyone knows what he has done,” said Tierney. “He has shone in every competition we have played in.

“He has a target in his head that he wants to get to this season – but he isn’t letting anyone know what it is! He obviously had a number in his head at the start of the campaign and he is keen to get to it but we are just delighted with the way he has been banging in the goals.

“He is scoring goals for fun just now and it’s great to see.

“It is ideal now that the window is closed because it means that the talk is more about what is happening on the park. We have kept all our players and that gives us the best chance possible as we look to go forward and be as successful as we possibly can be this season.”

Tierney himself has also attracted interest from elsewhere given the level of his performances not just domestically but in the elite environment of the UEFA Champions League.

The teenager is tied up on a long-term deal at Celtic and remains settled at the club he grew up supporting.

“I just concentrate on playing football. I don’t really take any notice of the other stuff. It is just about training as hard as I can and playing for Celtic. That was my dream growing up and it is amazing to be able to go out and do that.”