Both clubs will head to Australia in the summer for a London derby down under but the omission of Kane and Rice from the publicity pictures may worry supporters.
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The futures of both England stars remain unclear with talks to extend deals at their respective clubs, at a standstill.
Kane has just 15 months remaining on his current Spurs deal and as Manchester United, Real Madrid and Bayern Munich circulate for the England skipper, time is running out for his bosses to provide the reassurances needed for the 29-year-old to commit his future.
The club's social media posts announcing the friendly with West Ham featured Richarlison, Heung-min Son and Cristian Romero, which has not gone unnoticed by Spurs supporters.
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Hammers star Rice has also been linked with a move away this summer and Arsenal are among his admirers.
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Instead of Rice, Lucas Paqueta, Jarrod Bowen and Nayef Aguerd with are the men promoting the game.
Like Kane, Rice will be a free agent at the end of next season.
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While the tour posters offer no indication of their respective futures, it will worry fans nonetheless with both players expressing desires to win trophies previously.