The Mirror says Sturridge looks on his way out of Liverpool.
And it is likely that he will have to quit Anfield in January if he is to push for a place in England's World Cup squad.
Klopp conceded: "Physically, Daniel is in the best shape since I came. But, obviously, there are a few players around him who are not that bad as well!
“At the moment, there is absolutely nothing to say about the transfer window because tomorrow there could be one injury and Daniel could play the next five or six games."