Liverpool fans are technically correct when they say that it is Liverpool's call, from a strictly legal standpoint, as to whether Suarez is sold or whether he stays with the club. It's pretty much univerally accepted now that the "clause" in Suarez's contract doesn't force Liverpool into letting Suarez leave, quite what the point in the clause actually is at all seems a mystery, as it's given Suarez no power, officially, in this situation whatsoever. As for Suarez's claims that Liverpool promised him he could leave this summer, if they failed to qualify for the Champion's League, well that's not a legally binding agreement either. Personally I believe that a conversation along those lines probably did take place, whether it went as far as to be a shake hands agreement is debateable, but I believe Suarez was probably given certain assurances that are now not being adhered to (Liverpool, this time last year, had no idea quite how good a season Suarez was gojng to have, now he's had such an exceptional year they don't want to let him go). So yes, overall, Liverpool hold the cards here, legally.
The reason I reiterated "legally" in that last paragraph is to illustrate the differences between the legal position, and the real world position of this whole situation. Whilst Liverpool are in charge legally, it's a different matter in real world terms. Suarez wants to leave, his behaviour and his attitude, in pre-season have not been those of a player happy where he is, or motivated to give his best for his club. It is naivety in the extreme to assume that, come the start of September, if Suarez is still in a Liverpool shirt, he will be anything like the player that carried Liverpool's season last year. There are some players, like Bale, like Modric before him, that you can see knuckling down, accepting the situation, and giving their best, Suarez doesn't strike anyone as that kind of player. What Liverpool will find themselves with is a £40m+ asset who isn't giving them anything like that kind of value. Don't think that, as this is a World Cup year, Suarez will be forced into giving his best either, do you really think that Uruguay will be leaving him out? Seriously? He's a nailed on squad member for them, if they qualify, even if he has a seriously sub-par season at Liverpool. So, in real world terms, Suarez actually holds a great deal of power or sway in all of this. Ultimately he is 100% responsible for his influence on Liverpool's season, there's nothing Liverpool can do to make him give a shit, or put in high standard performances, that's all on him. The assumption, from Liverpool fans, and indeed from their management, that they can simply deny Suarez his wishes, and when the transfer window closes, he'll just say "ok, fair play gaffer, lets get on and try and make the top 4" is absurd. The 2013/14 Luis Suarez will not be the 2012-13 Luis Suarez, and if he isn't Liverpool will struggle to match last seasons 7th place finish, let alone attempt to break the top 4 (something I feel is way beyond them even with a motivated Suarez, but that's another point entirely).
Liverpool need to sell, and sell now, there is no scenario with Suarez remaining at Liverpool that ends well for the club. Get the £45m (which is what I think you can push Arsenal to) and use it to add 3 quality players in the £15m-£20m mark, Liverpool will be far stronger for it.