According to the Daily Star, Kane has told Tottenham that the club can't stop him leaving if he decides to move on.
The Reds and Gunners have always been linked with Lemar after his stunning form last term piqued their interest, and both are plotting moves for the France worldwide as replacements for Philippe Coutinho and Alexis Sanchez respectively.
The Hammers could miss out on the 26-year-old, though, after Valencia made a £12m offer.
Elsewhere, West Ham United are plotting a move for Arsenal midfielder Francis Coquelin, says the Mirror. Moyes is looking to strengthen his midfield and Sky says that the Arsenal pair are on a shortlist that also includes Joe Allen, Steven N'Zonzi, William Carvalho and Jonjo Shelvey.
That development will be welcomed by Arsenal if Arsene Wenger does decide to push forward with a move for Lemar. He said: "I don't know if City is in for anyone".
And his boss, Leonardo Jardim has hinted although subtly that the Ligue 1 Champions are ready to business this month, which opens the doors for both Liverpool and Arsenal. It now remains to be seen if the figure turns out to be prohibitive for either Arsenal or Liverpool, or if either club ends up signing him.
Liverpool are long-term admirers of the 22-year-old, but they are yet to make a bid despite having money to spend following the £145million sale of Philippe Coutinho to Barcelona.
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