Adrian Kajumba of the Daily Mirror reported Tuesday Kane has been ruled out "until May and faces a desperate battle to be fully fit" for this summer's tournament in Russian Federation.
Kane turned his ankle in a challenge with Asmir Begovic.
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If Smart is sidelined for an extended period of time (potentially into the playoffs), it would be a big hit to the Celtics. Boston Celtics star Kyrie Irving will not play in Wednesday's game against the Washington Wizards because of a knee injury.
According to reports in the British media on Tuesday, the injury is serious enough that Kane is facing a race against time to return to action in time for the World Cup in June.
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With Beau Allen set to become a free agent, the Super Bowl champion Eagles were in the market for depth at defensive tackle. Ngata was selected to five straight Pro Bowls from 2009-2013 and was a back-to-back All-Pro performer in 2010 and 2011.
That would mean Kane would return for the final few games of Spurs' Premier League season and would have only a few matches to build his fitness ahead of England's World Cup run in Russian Federation this summer.
He left the ground on crutches and had to postpone a scan due to the amount of swelling.
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Another surprise victor was Cyprus' Marcos Baghdatis, who beat Argentina's Diego Schwartzman, who is seeded 14th, 7-5, 6-4. Keeping it simple and maintaing a consistent plan of attack, Daniel worked Djokovic from corner to corner.
Kane, who has scored 35 times for Tottenham this season, would only have a handful of matches remaining this term to prove his fitness to England manager Gareth Southgate.