I kind of think the story is bs as well. But, let's for the sake of it say that it is not!
I think if I were in Klopp's position, I would say that at least one of Ings, Sturridge, Origi and Heskey needs to go. They've scored between 3 and 5 goals each this season. From a harmony standpoint, I would say that it's really between Sturridge and Heskey to go as the others would perhaps "settle" for time on the bench. Sturridge is a crock, and won't go anywhere. I also think he is a better striker than Heskey. So on that basis, that's why I think he would get rid of Heskey over and above Sturridge or the others.
With regards to his limitations, I just don't see the limitations that people are saying that he has. He's not lazy but if I have one worry it is that I am yet to see clever movement off the ball from him. Having said all of that, his scoring record can hardly be dismissed, and it is not as if he is not scoring goals for Liverpool. He's 25 and fit, and already has some comrades in our team. If the price were right, then I'd take the punt. It's not as if we would lose significant amounts of money on him, and if we're only buying him as a backup, there's no harm done there is there?
With regards to them cutting their losses after just spending some big money on him just 6 months ago, they do have precedent with that through Robbie Keane.