The Owls stopper had been heavily linked with a move across the border this summer, but Warne has said his side are targeting a Premier League loanee instead.
The 23-year-old only played twice for the Owls first team last season and will be frustrated at his lack of game time.
However, he will not be moving to Rotherham.
“I haven't had any contact with him or any conversation with (goalkeeping coach Mike Pollitt) Polly that he is in our top three,” the Millers manager told the Star.
“He isn't on my radar at the moment, I don't dispute he is having a good career.
“I don't understand where that rumour has come from.”
Having loaned Marek Rodak from Fulham for the last two seasons, Warne will again go down the route of signing a young stopper.
“I will definitely be signing a goalkeeper,” he added. “I personally like Under-23 goalkeepers. I like the way they are, I like the way they play, they are more aggressive off the line, they can kick with both feet.
“Marek was like a free signing for two years. We had an opportunity with a permanent signing, but we didn't investigate that further.
“The one we like is the one we want to wait for.”
Their number one target has been heavily suggested to be Leicester goalkeeper Daniel Iversen.
Warne added: “I am not comment on that for obvious reasons but he is one of that type. I do like him but I like a few. It would be amiss to say.”
The boss has confirmed that Anthony Forde is the last of the club's four wingers to leave the club.
Forde follows Joe Newell, Jon Taylor and Ryan Williams in turning new deals down at the club.
Warne said: “Forde isn't staying. Unfortunately I spoke to all four wingers during the season to try and get them to stay.
“I had a lot of time for all four of them but once we were relegated they all wanted to see what was out there for them, unfortunately that has been the case.
“They will all go on to different clubs with my blessing. It is a big miss for me, all four played a big part for me across different seasons but they will go somewhere else.
“What we have built here is about the dressing room and if anyone doesn't want to play here than can go somewhere else.”