Spurs could be set to be without their all-time record scorer as links with a move to Bayern Munich continue to hang over his future.
Kane starred in their 5-1 pre-season friendly win over Shakhtar Donetsk on Sunday by scoring scoring four of their goals.
Next Sunday will see Spurs play their first game of the new Premier League season when they travel to Brentford.
After submitting an £86million take it or leave it offer to the north London side, Bayern gave them a deadline of Friday evening.
It seems to have been ignored by Spurs though, with Kane still in Postecoglou's plans for the upcoming week.
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When asked if he's planning for Kane to make the trip to Brentford, he said: "I am just planning for preparing the team for Tuesday and then we'll work our way into Brentford for next week.
"I haven't even thought about who will start that game. It is about trying to have as many players ready for that fixture as possible and we've still got guys coming in.
"We signed young Ashley Phillips on Friday and he'll train with the first team. We hopefully have another couple coming in over the next couple of days.
"All those kind of things are part of the planning and I'll deal with the team for Brentford at the back end of the week."
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He also addressed Bayern's continued efforts to sign their star man, who could leave the club for free at the end of his contract next year.
When asked about the Bundesliga champions' public approach to the potential move, he said: "I don't have a view either way mate. That's up to Bayern to decide.
"If that's the way they want to conduct things, it's not up to me to judge that. It doesn't affect me. I don't sit there on a daily basis and worry about what other clubs are doing.
"I think what is factual right now is that he is a contracted player of our football club.
"I certainly wouldn't talk about contracted players at other football clubs but I'm not at Bayern mate so they can go the way they want."
Should he leave, Kane would depart Spurs after scoring 280 goals across all competitions, with 32 of those coming last season.