He spent years with Wigan and Everton before taking the reins of Belgium, who are now ranked No 1 in the world.
Spaniard Martinez is believed to be on Spurs' shortlist but they are unlikely to be the only suitors, says The Sun.
And Tottenham chairman Daniel Levy is in no rush to appoint a successor to axed Jose Mourinho.
But while Martinez is under contract, it would not be difficult for him to leave after the Euro 2020 finals this summer.
Martinez has trusted backroom staff who could take pre-season training at Spurs while he is with Belgium.
He has worked with top Belgian talents such as Kevin de Bruyne and Romelu Lukaku.
But the chance to get back to daily involvement appeals to him.
As someone who plays a passing style admired by Spurs, they could be a good match as Levy seeks a coach to please fans.
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