The Sun says Klinsmann is keen on returning to Europe from California, where he now lives.
Liverpool's American owners George Gillett and Tom Hicks like the wholesome profile Klinsmann has.
And, though Klinsmann is very much his own man, he would be easier to keep in line than Benitez.
The Spaniard's relations with the American pair remain fragile - the manager wants to establish transfer targets in the January window but feels Gillett and Hicks have been dragging their heels.
But Liverpool are feeling the squeeze and it is more likely Benitez will lose players rather than gain any.
A source close to Klinsmann said: "Jurgen is ready to get involved in football again.
"He loves it in California but, when you are such a big figure in the game, you cannot stay away from it for ever."