Wilks, a former Doncaster Rovers and Barnsley man, has been high on the Owls’ wishlist for most of the summer.
The Star revealed last month that the 23-year-old has gone as far as to agree outline personal terms with Wednesday.
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But the two clubs remain at loggerheads over a fee, with little moving in terms of progress despite a growing optimism from sources close to the deal some weeks ago that the deal was getting close.
While Wednesday boss Darren Moore has chosen to keep his cards close to his chest over the saga, things have played out publicly at the Hull end.
Tigers vice-chairman told the Owls to up their valuation of Wilks – whose contract is set to run out next summer – or risk losing him to interested parties abroad.
That was nearly a month ago and he remains a Hull City player.
Wilks’ absence from Hull’s squad in the latter stages of their pre-season campaign raised eyebrows and he was nowhere to be seen for their Championship win over Bristol City on Saturday.
But Tigers boss Shota Arveladze has confirmed this has been down to a minor muscle issue and said he expects the attacker to re-join the squad for their trip to Preston North End this weekend.
More to the point, Arveladze expects him to remain a Hull player beyond the September 1 transfer deadline.
“I am not expecting him to leave, I am expecting him to use all his energy to play with us,” he said.
“He had a good pre-season. Unfortunately, he missed eight days because of a small pain. Now he is back again and I hope he gets his chance, whether that is 10, 25 or 45 minutes.
“I never wanted him to leave. It is his turn to show he wants to stay and play.
“It's always positive that if people want to buy our players,” the Hull boss continued.
“He does well in the training sessions and I think he had a good game on Saturday. If I saw him slipping I would talk to him but he is fully concentrated.”