I don't think its even Sturridge's fitness that would be Klopp's issue, its the fact that pressing, physically occupying and out-muscling defenders is not something that he consistently displays a willingness to do.
Loathe as I am to jinx it, I don't think he's had such a long spell of fitness since he's joined us, and this spell was the aim of the surgery he had last summer. There were reports at the time that he'd be in for another run of months in which he'd pick up niggling injuries, and then the improvements would start to show.
His pace and acceration is coming back game by game as well. If he can stay fit until the end of the season, I see no reason why we should just assume that he'll go back to being unreliable when the underlying issue may well have been fixed, to some extent at least. Plus, we finally seem to have a good alternative in Origi to take the importance away from Sturridge, so its not so damaging when he is unavailable.
I'd much, much rather we sign an alternative to Sturridge than a replacement. He's a brilliant, brilliant striker. We'd be very fortunate to replace him with somebody anywhere near as effective he is.