Postecoglou was installed as the new favourite to become the next Spurs manager on Thursday amid reports he is being “strongly considered” for the post after the previous frontrunner, Feyenoord boss Arne Slot, pulled out of the race.
Former Spurs midfielder Ryan Mason is currently in interim charge having replaced Cristian Stellini, who stepped in when Antonio Conte parted company with the London club in March. Spurs sit eighth in the Premier League with one fixture remaining away to Leeds United on Sunday, with qualification for the Europa Conference League still in the balance.
Postecoglou has guided Celtic to a second consecutive Scottish Premiership title this season - securing Champions League group-stage football again next season - and will secure a domestic treble if his side defeat Inverness in the Scottish Cup final next weekend having already lifted the League Cup.
Asked about the Spurs speculation by Sky Sports, the Celtic boss replied. "And yet I'm still here. It doesn't [come onto my radar]. I think anyone who knows me, I've been asked about these things plenty of times, know that what's important for me is the here and now. I've never planned anything in my football career. My ambitions right now are to enjoy tomorrow, have a good game, then try to win a cup final and try to make it a special year. It's not every year you get the opportuntity to win a treble. If anyone thinks I'm thinking anyhting other than that, they don't know me."
Celtic will lift the Premiership trophy after the final match of the league campaign at home to Aberdeen on Saturday. Asked whether he has pondered his future beyond the end of this season, Postecoglou added: "No, because I know that's not how football works. You can't as a manager try to chart a course for yourself to be in a certain position at a certain time. The one thing I do know for certain 100 per cent is that if you're not concentrating on the task at hand your destiny gets taken out of your own hands. I've worked really hard in my career to not be in that position and the way I've done that is to make sure that beyond what happens this week, and we've got a couple of big games, I'm not going to think about anything other than that. Whatever happens in my career from here onwards will happen because I'm doing what I do really well."
Given the opportunity to send a message to Celtic fans who may be anxious over the prospect of losing a manager who has delivered four trophies and will bid for a fifth at Hampden next weekend, Postecoglou said: "I think what the Celtic fans want is their manager to be concentrating on what's important to them now. I hate to think that our supporters want me thinking about anything else other than having a great game tomorrow, having a great day, and then winning a cup final and making it a treble which will make it a special year. I think that's where they want my responsibility to lay."