With the World Cup just three months away, national coach Gareth Southgate will also be eager to find out how long Kane could be sidelined for.
A Tottenham source revealed the injury is as serious as the one that kept him out for seven weeks from September 2016.
He will then miss the semi-finals if they win and four league fixtures after the worldwide break, a potential top four decider against Chelsea and further clashes with Stoke, Manchester City and Brighton.
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Gareth Southgate is set to name his squad for this month's worldwide friendly matches against Holland and Italy, but Kane will be absent for both ahead of this summer's showpiece.
Tottenham are back in Premier League action following the global break with a trip to top-four rivals Chelsea on April 1.
According to the London Evening Standard, Pochettino now plans to go without a recognised striker up top during Kane's injury absence, which could span a couple of months.
Given the delay in getting a full diagnosis of this latest problem, it looks highly unlikely that the 35-goal striker will be fit for Spurs' FA Cup quarter-final at Swansea on Saturday.
England play Nigeria and Costa Rica in pre-World Cup friendlies early in June, then kick off their group phase campaign against Tunisia on June 18 before further group matches against Panama and Belgium.