Daniel Levy met Bayern Munich chief executive Jan-Christian Dreesen on Thursday to discuss the possible transfer of Harry Kane.
Sky Sports News has been told no meaningful progress was made but dialogue remains open. This is not the first time Levy and Bayern have met or spoken.
Tottenham will continue to try and persuade Kane to sign a lucrative contract extension but fear he will leave for a Premier League rival should he run down his current deal.
Kane has not ruled out any option at this stage and will be part of the Tottenham squad that departs for their pre-season tour to Australia on Friday.
Postecoglou has made it clear that he plans to shape a side that produces exciting, attacking football and would like Kane to be part of it.
Should he start the season in England it will give the club a chance to show him and other senior players that there can be a more positive outlook than recent years.
Bayern believe Kane wants to join them and that appears to be his most likely destination if he departs in the coming weeks. Tottenham have made it clear they do not want to sell their record scorer and certainly won't entertain the £70m figure Bayern are willing to pay.
The England captain has scored 213 goals for Spurs and is the second-highest scorer in Premier League history behind Alan Shearer. He needs 48 more goals to break the record.
Kane scored an impressive 30 league goals last season as Spurs could only finish eighth.
One thing that is clear is Tottenham will not sell to an English club in this transfer window, ruling out a move to Manchester United, with Erik ten Hag shifting his focus to Denmark striker Rasmus Hojlund.
Postecoglou: No guarantees over Kane future
Postecoglou said at his first Tottenham news conference on Monday that he had received no guarantees over the future of his star player. "No, I haven't had any assurances [over Kane's future] and I wouldn't expect any assurances because with these kind of things you're never dealing in definites or certainties.
"I'm trying to concentrate on the things that I know right now, and what I know right now is that Harry's part of this squad. He's looking forward to coming back to training, getting among the players back in here and we start working together.
"If I spend too much time worrying about the impact that it may have either way, I'm going to miss trying to build a team because ultimately that's what's going to make us successful.
"If we build a team that plays football a certain way. I'm not going to miss this initial opportunity to lay down what I know is going to be important in the long term.
"What's important in the long term goes beyond individuals. It's more about overriding philosophy on who we want to be as a team and the key people within that."
Speaking ahead of Wednesday's meeting with Kane, Postecoglou said: "I don't think it is my role to sit there and sort of treat people in a manner because of their circumstances. I am big on treating everyone the same.
"Harry is already part of the history of this club and I want him involved here. My conversation with him will be about how we can make this club successful and that is what he wants as well.
"I doubt it will be defining in the manner people think. I want to introduce myself to Harry, give him my vision, get an understanding from him over what his vision is and try be successful."
Postecoglou officially started his new role as Tottenham head coach on July 1, but he's been working hard behind the scenes for nearly a month already.
Since the announcement of his appointment was made on June 6, the Australian has been planning thoroughly for what appears to be a huge job at Spurs, who face the reality of no European football for the first time since 2010.
[SkySports]