Former England international Davies is looking for a new club after being released by Bolton Wanderers at the end of last season.
A reunion with Owen Coyle at Wigan Athletic has been ruled out, but fellow Championship clubs Blackpool, Burnley and Millwall have been linked with an offer.
Davies has spoken to Jones about a possible deal at Hillsborough and the boyhood Sheffield United fan previously confirmed he is open to the prospect of joining the Owls.
Jones is waiting to see how the situation develops, but the Owls boss would relish the chance to have the 36-year-old in his squad next season.
"At the moment we're keeping all our options open," said Jones in the Sheffield Star.
"We're just waiting on certain things and for the chairman's green light on one or two other things, 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.
"But no decision has been made yet; the chairman is away at the moment, we're in Burton; when we come back we'll get our heads together and see where we are."