The centre back was on loan at Wolves earlier in the season, but it is claimed that at present despite this, he is equally open to a switch to the Owls.
Williamson has not ruled out the possibility of staying at Newcastle United either, despite the Toon being open to offers.
SkySports report: "Press Association Sport understands Williamson does not have a favoured club and is yet to discuss personal terms with either.
"It is also understood any move is not set in stone and the 32-year-old could yet remain at St James' Park to see out the rest of his contract, which expires in June."
Many Newcastle fans had hoped Williamson would have been moved on last summer after becoming a scapegoat for their poor form last season.
He has been on the periphery this campaign, loaned to Wolves, before being recalled amid a defensive injury crisis. He has not featured over the past few weeks due to a muscle injury, but is expected to be fit again shortly.
Wednesday are currently five points above Wolves in the Championship table, with both sides within reach of the play-off places.