I watch Wigan most weeks, as a neutral fan who is partial to them - and let me tell you, Wigan have players nowhere near good enough to play in the Premier League in massive parts of their squad.
Al Habsi, Figueroa, Moses and James McCarthy are the only players who would get into a decent PL side (ie. someone like Fulham). His job this season has taken huge balls and it's something called 'the long game' - perhaps something that Liverpool fans have given up on in the past few years.
Wigan deal with the same problem of having to rebuild the team ever year due to a combination of their best player leaving and having no money to spend whilst teams around them all usually spend to try and not be in the relegation battle again.
The only way they were going to stay up was the way they did - By practising the Martinez style and sticking with it. They've got small players, so no chance of long balling it or bullying themselves through games.
If you actually watched Wigan in the first half of the season, they were very good in most games for the quality of player they had, and you saw progression through the season.
A side without the players to stay up managed to by finally seeing the fruits of their labour, all of which the manager orchestrated by getting fairly poor players (Gary Caldwell, Beausejour, Maloney, Di Santo) to understand his system and style of play well enough. In the end, they were beating top sides for fun. But once the likes of McCarthy and Moses move on, they're back at square one, and this is why they have to struggle for large parts every season.
He wouldn't have that problem at Liverpool imo, they have players far greater than Wigan, not world class, but competent, solid Premier League players, as long as they listened, they should do alright. Furthermore, Liverpool can hold onto a good number of top players, and also have resources to replace them if they do leave.
I would make a further case, but frankly, I'm not arsed about Liverpool, I'd rather he stayed at Wigan, he's loved there. It's hugely unfair criticism of him I'm seeing though.
Above I saw that he shouldn't be appointed because the fans won't take to him. Christ alive, and people talk about Player Power? Fans are soft as ***** these days. I'm a Newcastle fan, and even though Mike Ashley is a very jowly man with questionable morals, we've seen first hand the merit in not listening to fans on these matters, and Liverpool fans would be pretty happy if next season they played as Newcastle have all season, especially considering you could do it with a much bigger squad.
Very few who watch Wigan and Liverpool would say it's likely he'd fail there. I would ask how many of the Liverpool fans clamoring for Klopp or another 'name' have really watched a lot of Dortmund, but I doubt it's a lot. Klopp would be a good choice (other 'names' wouldn't), but it's strange how fans pass judgement on who their club should get based on very little in depth knowledge of these people.