Harry Kane will consider leaving Tottenham if the club decides to accept a transfer fee but won't force a move away this summer, sources told ESPN.
Earlier this month, ESPN reported that Kane had no intention of signing a new contract at the Premier League club.
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According to sources, Spurs had been hopeful of staving off interest from Bayern Munich, Paris Saint-Germain and Manchester United by tying down Kane on a long-term basis, given he has just one year left on his £200,000-a-week deal.
However, his refusal to agree a fresh deal places renewed pressure on Spurs over their reluctance to let Kane, who turns 30 next week, leave the club.
Chairman Daniel Levy values Kane at around £100 million ($128.5m) but would prefer not to lose his star striker as new head coach Ange Postecoglou begins work at the club.
But Spurs risk losing Kane for nothing in 2024, and a big offer from one of Kane's suitors could force a rethink. Bayern have so far had two bids rejected, the second of which was worth around £70m.
United are interested in Kane but as yet have not made a formal offer out of a belief Levy will make any deal too difficult.
Significantly, Kane is not pushing to leave, and sources told ESPN that it remains possible he could stay at the club and even agree terms on a new deal towards the end of next season if the club are successful under Postecoglou.
However, Kane is open to leaving if Tottenham decide they want to let him leave and is thought to be willing to move abroad with Bayern remaining confident they could lure him to Germany.
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The club have held at least one meeting with Levy, while reports have suggested Bayern coach Thomas Tuchel met with Kane to discuss a move.
Bayern's honorary life president Uli Hoeness said last week: "Harry Kane has clearly signalled in all conversations that his decision stands -- and if he keeps to his word, then we'll get him, because then Tottenham will have to buckle."
However, Bayern remain short of offering a financial package that will convince Spurs to part with their all-time leading goal scorer.
Spurs continue their preseason preparations in Thailand this weekend with a clash against Leicester City on Sunday.