The Spurs gaffer is also keen on landing David Villa from Barcelona according to the paper, and wants his club to launch a £45m raid to bring in the prolific pair.
Tottenham paid the price of not adding to their front line last season as they missed out on Champions League football by a point to rivals Arsenal.
Jermain Defoe and Emmanuel Adebayor were the club's only front-line strikers last term and both spent spells on the sidelines through injury, leaving Spurs looking short in attack.
The Independent report Villas-Boas is keen to remedy the problem early on in the transfer window, and has identified Martinez as another potential target, along with Villa, in a combined £45 million deal.
Brazil forward Leandro Damiao has been a target for the north London club for some time, but Villas-Boas is wary of missing out on the Internacional man once more and has moved to identify other potential recruits if a deal can't be done.
It would be a surprise if AVB's recommendation of Martinez results in a deal being done; Porto are under no obligation to sell after letting Joao Moutinho and James Rodriguez join Monaco for a combined €70 million.
The Colombian cost Porto €7 million last summer and was the Portuguese league's top scorer with 26 goals this season.