At the time, Kane was playing under former Spurs boss Tim Sherwood, who Dyche revealed was the one to price Burnley out of a move for the striker.
"I phoned up about him and at the time, I think it was Tim Sherwood, immediately said £7m and we were in the market for like £3m," Dyche told The Fozcast.
Podcast host, former Manchester United and Watford goalkeeper Ben Foster, scoffed at Tottenham's asking price for Kane, who at the time was a relatively unknown youngster.
"Unproven, exactly, and you're Burnley. I went to the board and they said 'we can't do that'," Dyche added.
"Now you might have even got, I don't know, five plus add-ons but at the time we were looking at I think George Boyd [who would become] record signing at the time for like £3m, so we just couldn't do it.'
"But Harry Kane, I always thought he was an amazing player and still do now."
While Kane made his first-team debut for Tottenham in 2011, his breakthrough season came in the 2013-14 campaign under Sherwood when he made 19 appearances in all competitions.
He would become a first-team regular the following season, scoring 31 goals in 51 games for Tottenham under Sherwood's successor, Mauricio Pochettino.
Kane has since gone on to score 189 goals in the Premier League, while he has also bagged 50 goals in 78 appearances for England.
It could be have been a very different story for the striker had he moved to Turf Moor.
Dyche, meanwhile, has hit back at claims he only tried to sign British players while in charge of Burnley.
Speaking on the SPORTbible Stories podcast, Dyche said: "There's popular misconceptions about that sort of stuff. There’s loads of myths, you know what I mean?
"I don't like foreign players, it's all rubbish. Of course I love foreign players, why wouldn't you? They're just players. You want players who are good and make you better.
"We just didn't have the resources at Burnley, or the mindset from the old board. More so from the new board, to do that."
SPORTbible Stories is the brand-new podcast from the SPORT team at LADbible. The first episode features a chat with former Burnley manager Sean Dyche as he opens up on his departure from Turf Moor, what the future holds and the amazing story of the spin wheel for fines while in charge of the Clarets. You can watch the first episode here.
Featured Image Credit: Alamy
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