The Daily Mail reports that after the initial approach, both sides agreed to revisit the situation once Kane's World Cup participation is over. However, the strong indication from Kane's camp is that the priority after the tournament will be agreeing a new deal at Bayern rather than pursuing a move to Barcelona.
Kane, 32, has one year remaining on his contract at the Allianz Arena, where he has won two Bundesliga titles and the German Cup. He scored 61 goals in 51 games for Bayern Munich last season and has added three more in the group stage of the current World Cup, where he became England's all-time leading scorer at a tournament with his header against Panama.
England face DR Congo in the last 32 in Atlanta on Wednesday, and Kane remains fully focused on the knockout rounds before giving any thought to his club future.
Barcelona are in the market for a new striker following the departure of Robert Lewandowski and see Kane as the ideal replacement. Sources have indicated the club are prepared to go all out should there be any encouragement that a deal is possible, though Bayern would vigorously resist any attempt to sign their star player.
The picture will only become clearer once England's tournament concludes. For now, the conversation has stalled before it truly began.
Kane's record in Germany has been extraordinary, and with another year on his contract, Bayern hold all the leverage in any negotiation. They would demand a fee commensurate with that status, adding another obstacle for a Barcelona side that must also find creative ways to fund the sort of deal that would be required to prise away the Premier League's most prolific striker of the modern era.