According to Portuguese newspaper A Bola, the Gunners manager has lodged a €9.5m bid for the 20-year-old Batshuayi.
But should Standard Liege turn that down, Wenger will look towards Porto ace Martinez. The Colombian international has a €40m release clause and would require a much more significant investment on the part of the Arsenal board.
But the report claims Arsenal are ready to spend big in January. With 39 points at the half-way mark in the Premier League season, the Gunners sit top of the table - one point clear of Manchester City.
And Wenger is keen to carry the momentum into the New Year. The January transfer window gives him an opportunity to address some of the weaknesses in the squad, with another striker thought to be a priority.
Danish international Nicklas Bendtner is the only alternative to Olivier Giroud as an orthodox striker, and the arrival of the €40m-rated Martinez would certainly make a statement heading into the second half of the campaign.
But if possible Wenger wants to avoid another massive spend on a single player - following the £42.4m acquisition of Mesut Ozil in August.
As a result, Belgian under-21 international Michy Batshuayi remains his first-choice target up-front.
He's managed 13 goals in 17 league starts for table-topping Standard Liege in the Jupiler League so far this term.