Wolves coach Kenny Jackett has moved to address the rumours over Hennessey's Molineux future, explaining that they have not yet received any interest from other clubs.
"In terms of the overall picture we haven't heard from any clubs or had any bids in yet," he told the club's official website.
"We don't know whether there is anything imminent but we are not close to anything as we haven't had a bid.
"In terms of Wayne he will carry on as a Wolves player until something changes - we haven't had any calls as yet and he will carry on as per usual."
Jackett also revealed that Hennessey has now apologised and accepted full responsibility for his actions prior to the Wolves' game 1-0 defeat to Gillingham on Friday.
The goalkeeper chose not to make himself available for selection, despite the news that Carl Ikeme faces up to six weeks out with a broken hand.
But Hennessey has since apologised for his actions, with the club taking disciplinary action ahead of Saturday's visit of Preston.
"With hindsight he wishes he hadn't said what he said and I am sure he will speak for himself but to me he has apologised and said it was wrong," Jackett said.
"There will be some internal discipline and once that has been dealt with we will move on and put it down to an error of judgement.
"He is available for selection and will have no problems going forward as a Wolves player.
"He is taking full responsibility for what happened and not turning around and saying somebody advised him - perhaps he wasn't in full possession of the facts.
"Overall it was an error of judgement and the wrong thing to do and I was surprised and shocked at the time.
"But the fact he has arrived today in a different frame of mind and he will be disciplined internally and we all move on."