The 36-year-old striker is currently a free agent following his release at the end of the last season from Bolton Wanderers.
Having not added any fresh faces to his squad so far this summer, Jones is eager for the former England international to be his first signing.
"At the moment we're keeping all our options open. We're just waiting on certain things and for the chairman's green light on one or two other things," he told the Sheffield Star.
"Then we can move and if that involves Kevin Davies it will be fantastic, because he's a quality player, a senior player, and he'd be good on and off the pitch."
Davies has also been linked with Burnley, Blackpool and Millwall.