Of the two, Martinez is apparently in the lead for the job and is currently in talks with Liverpool owners, Fenway Sports Group (FSG) in United States.
One can only hope that this is just another formality in the long and arduous search for a new manager and not a prelude to an appointment. If appointing Kenny Dalglish after sacking Roy Hodgson in 2011 was a PR victory with the club's supporters, bringing Martinez in would be nothing short of a disaster.
There is already a considerable amount of opposition to the fact that Martinez is even being considered for the job and one can only imagine the criticism and pressure that will be leveled at him each game Liverpool dont win.
For someone more accustomed to fighting relegation battles, this will come as both a shock and a sobering reminder that expectations at Liverpool are far different from that at Wigan.
But maybe I'm getting ahead of myself here.
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The idea of putting Van Gaal in that position seemed to indicate that FSG wanted the Dutchman to implement a new transfer policy and bring in some fresh talent to provide some much needed change to the squad.
It also meant that high profile managerial candidates - Fabio Capello, Rafa Benitez - were out of the equation. Van Gaal is quite the imposing figure (he's also 60) and only a young an inexperienced manager like Martinez would be able to work with him.
Besides, Van Gaal would be some sort of insurance for FSG should Martinez fail and could be called in to step into the manager's role if needed.
But as it turns out, Van Gaal has indicated that he is more keen on the manager's position at Liverpool than the technical director's post.
Despite being sacked by his last club, Bayern Munich, Van Gaal possess an impressive resume that includes a Champions League trophy, UEFA Cup and several league titles in Holland, Spain and Germany respectively.
Simply put, if the choice boils down to either Martinez or Van Gaal, it should be a no brainer.
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Just as successful as Van Gaal, Capello has a keen understanding of the English game and would not need time to settle in.
And if all else fails and you're left with just Martinez, I would rather go with Benitez who at least knows what it takes to compete at the highest level (and FSG wouldn't have to pay him to relocate. He already lives in Liverpool!).