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 (opens in new tab), 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 (opens in new tab) 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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