Kane has also been linked with the Blues since reportedly informing Spurs of his preference to leave the club at the start of the summer.
After the England captain missed his first few days of pre-season training, he is now being put through his paces in isolation after returning from holiday.
Pep Guardiola has confirmed his interest in the 27-year-old, but only if Levy is willing to play ball and come down on his £160m valuation.
Still, if boss Nuno Espirito Santo stands to lose a player like Kane, who finished last season with the most goals and assists in the Premier League, Martinez represents a fantastic option.
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