The 33-year-old has a year left on his contract at Nottingham, but has been linked with a return to Preston, who he has made 470 appearances for.
Lindsay told the Evening Post: “We haven’t made an enquiry about Paul McKenna.
“I was with the Forest chief executive at the FA’s AGM last week and we chatted about a number of things.
“Paul McKenna was mentioned just because he used to play here, but there was nothing more to it so I was quite puzzled when I saw we were being linked with him.
“Paul served Preston so well and is a great character. But we have a lot of midfielders in the squad and have to bear in mind his age too. We want experience in the side but also have to build for the future.”