Wednesday chief executive Alan Sykes met the former Sunderland boss in the hope of persuading him to succeed Terry Yorath at Hillsborough.
But Reid has turned the job down, telling Wednesday's official website www.swfc.co.uk, they were the "right club at the wrong time".
Sykes said: "The discussions we held with Peter were open and cordial throughout.
"We had an excellent, very constructive meeting. We discussed our situation and his and we also talked about the financial position of Sheffield Wednesday in terms of what was available for players.
"We never discussed personal terms, but he assured us that if he had wanted to join us he would have been sensible in that respect.
"But after giving full consideration to the situation, he indicated to us that he considered Sheffield Wednesday to be the right club at the wrong time.
"It is a club he would like to manage, but when it is enjoying better circumstances.
"It speaks volumes for Sheffield Wednesday and its supporters that a manager of Peter's standing and reputation was prepared to meet us and take the time to give us a considered response.
"He was our number one choice if he was prepared to manage Sheffield Wednesday."