City reportedly had one bid in excess of £100 million rejected last month, and they were said to have upped their offer this week.
However, according to Manchester Evening News, club sources have rubbished talk of a fresh, Premier League record bid. City were also said to have prepared a £400,000-a-week contract for Kane.
This comes after suggestions earlier this week that one of Gabriel Jesus, Riyad Mahrez, Bernardo Silva or Raheem Sterling could be offered as (one hell of) a deal sweetener in any potential move for last season's Premier League Golden Boot winner.
Will this latest development put to bed speculation over Kane's future? Almost certainly not; after all, he did tell Spurs at the end of last season that he wanted to leave - and nothing has come out so far to suggest that he's done a U-turn.
New Spurs manager Nuno Espirito Santo seems very confident that he will have the 27-year-old at his disposal for the big kick-off in a few weeks' time, though, telling the media last week: "Harry is our player, period. No need to talk about anything else.
"I have no doubts in my mind [about Kane's future]. I have no doubts."
Famous last words? Well, the window doesn't slam (why does it always have to slam?) shut for another 39 days, Nuno...
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