The company, whose founders include LA Dodgers baseball team co-owner Todd Boehly, had said two weeks ago that it was at the preliminary stages of assessing a cash offer for the North London club.
Tottenham, who need to raise money for a new stadium, have denied media reports that owner Joe Lewis was seeking to sell the club.
"Cain Hoy has subsequently terminated its assessment and accordingly is no longer considering making an offer for Tottenham Hotspur," the investment company said in a statement.
Had a deal gone through, Tottenham would have joined Manchester United, Arsenal, Liverpool, Aston Villa and Sunderland as Premier League teams with American owners.
(Reporting by Alan Baldwin; Editing by John O'Brien)
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