While that may be a poor decision on Arsenal's part, it's an interesting proposition for the Reds.
Here you have a guy who has had three separate incidents in which he's been banned for at least one game since October 2011, but also posted 23 goals in the Premier League last season. He's irreplaceable for the Reds on the pitch, but he could become a pain on and off it if Liverpool doesn't sell the 26-year-old this summer.
As ESPNFC's Mike Whalley noted, Suarez has publicly said he would like to leave the Reds. Although he has yet to hand in a transfer request, it's obvious that he's not very happy at Anfield. Who knows how restless (and reckless) he could get on the pitch next season if he's still with Liverpool.
Daniel Sturridge was second on Liverpool with 10 goals last season in the EPL. That's quite a drop-off from Suarez. Then again, you don't want a disgruntled player undermining your club's intentions to improve.
There's also the fact that Liverpool finished seventh in the Premier League even with Suarez being on the pitch for 33 games. The club is probably more than a piece or two away from legitimately contending for the Premier League crown. In that regard, perhaps it makes sense to deal Suarez for a large sum in hopes of acquiring several players who could eventually guide the club to the promised land.
Of course, that's hard to do when fans and media alike saw the impact Suarez could make last season. Losing a talent like Suarez could be looked at as a failure by the club. That would put even more pressure on Liverpool to win soon, even if that may be unrealistic.
In the big picture, Suarez has actually become more of a pain than a difference-maker for the Reds. The problem is, he's the only elite goalscorer they have.
So what does Liverpool do? Let us just be happy that we aren't the ones making the decision.