Kane was due to fly to Germany later to seal what will be a Bundesliga record 100 million euro deal with Bayern Munich.
"I don't have a blow-by-blow account of the whole thing but my understanding is that it's progressed to the point where it looks like it's going to happen," Postecoglou told reporters ahead of his side's Premier League match at Brentford on Sunday.
"That's all the information I kind of have at the moment and from that perspective it gives us some clarity that barring something unforeseen happens we move forward without Harry."
Postecoglou said he understood the deal was imminent and "certainly with training today and preparing for Brentford we're doing it without Harry.
"You kind of get an indication there that he had kind of made up his mind that if the clubs agreed, that he would go," he explained.
"There's been nothing along the way that's made me feel there's anything other than this outcome.
"Whatever I was going to say wasn't going to be relevant to how he felt, being here for the last month. I could plan this grand vision but I'm sure he's heard it all before."
"We've been planning for this, fair to say, for a while," added the Australian, who arrived at Spurs in June after the North Londoners finished a disappointing eighth in the league.
"A lot of our business up until now is with that in mind so this doesn't change things dramatically from my perspective, in terms of what we're trying to build," he added.
"Our whole strategy has been around the fact that Harry wasn't going to be around, more than likely. So it's not like we've had a pow-wow this morning and what do we do? We knew it was coming."
Postecoglou said Tottenham still had a big squad and there would be some more movement.
"I think some players will seek opportunities elsewhere and there's still three or so weeks to go in the transfer window... that's not because Harry's gone, that's always been in the plan.
The Australian paid tribute to Kane and said his record spoke for itself.
"I'm only new in the building, mate. I'm certainly not a spokesperson for this football club in the sense of proclaiming people's status but I think it's fairly evident Harry Kane will always be one of the greats."
