British media reported that the Australian is Spurs' next target to replace Antonio Conte, who made an acrimonious exit from the Premier League club following his outburst in March.
Postecoglou said the reports were nothing more than speculation and that they would have no impact on how he prepares for Saturday's final against Inverness Caledonian Thistle.
"This time last week it was a different story. It was somebody else linked. That's just the way it works," Postecoglou told reporters.
"It makes no difference to the way I behave or think or prepare. I didn't wake up thinking about anything other than getting training right and making sure we are ready for Saturday.
"Saturday means everything to us, everything. So it doesn't enter my sphere that I am going to be distracted - as I hope the players wouldn't be - by matters in their own lives."
Postecoglou, who is on a 12-month rolling contract, said he has not thought about life after Celtic while adding that managing in the Premier League was not a long-term goal.
"This football club plays in the Champions League, like everyone else I want to be competing at the highest possible level, wherever that may be," he said.
"That's how I got to a World Cup with Australia because I wanted to test myself against the best teams in the world.
"It (the Australia job) landed on my doorstep at the right time, because there's so many things that need to be aligned for these things to happen."
