Bayern Munich tabled an £86m bid for the England captain last week and set a deadline of Friday for Tottenham to respond.
No response has come from the English side and Kane was heavily involved in Tottenham's latest pre-season friendly on Sunday as he scored four times in a 5-1 win over Shakhtar Donetsk.
Postecoglou said afterwards that Kane remains a key component of Tottenham's plans for the upcoming season.
Speaking to reporters after Tottenham's latest pre-season outing, Postecoglou said: "You saw today that Harry Kane certainly is invested in what we're doing — and we will keep on doing that unless something changes. We know there's one deadline: that's the end of the transfer window."
“Beyond that, I’m in open dialogue with Harry and with the club on a regular basis. I’ve said to them that if the status quo changes then inform me.
“I don’t need to know about the comings and goings in between. I just want to deal with what’s in front of me because, irrespective of the outcome of that, I’m building a team here. I can’t wait (around) for a decision either way to get going.
“We don’t have the time or the luxury to do that. I’m working with what’s in front of me. You saw today that Harry certainly is invested in what we’re doing and we’ll keep on doing that unless something changes.”
Kane has only one year remaining on his contract with Spurs.
