The Champions League runners-up will pay £15m to bring the teenager to north London.
Clarke was promoted to the Leeds first team by Marcelo Bielsa last summer.
The York-born forward was then a regular throughout the 2018/19 campaign, making 22 appearances as the club qualified for the play-offs.
However, their failure to win promotion to the Premier League means Leeds are unable to keep hold of the highly-rated prospect.
And Tottenham hope to get the deal over the line in the coming days.
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