The former Sheffield United boss, who left Leeds in April, was on a five-man shortlist for the job and held talks with Owls chairman Milan Mandaric on Thursday evening.
Warnock is a boyhood Sheffield United fan and managed the Blades between December 1999 and May 2007. He also made derogatory comments about United's city rivals in 2002.
It was this affinity to the Bramall Lane club that played a huge part in his decision to snub the Owls, who are currently languishing in the relegation zone in the Sky Bet Championship and looking for their sixth manager in just over seven years after sacking Dave Jones last weekend.
"I did speak to Milan Mandaric last night (Thursday) and I think we both realised then that it wasn't going to be," Warnock told talkSPORT.
"When Milan phoned me originally I did tell him it would be pretty much impossible to manage Sheffield Wednesday when I'm a Blade, but he asked me to have time to think about it. He wanted me to try and keep them up.
"He has tried to bring me in as his manager about four times over the last 20 years so I have got a lot of respect for him.
"I have been pleased about the number of people in Sheffield, Sheffield Wednesday fans as well, that wanted me. But I think it's time to put myself to bed."