Former Aberdeen defender Hart came close to joining Hibs in January before Alan Irvine was replaced as North End manager by Darren Ferguson.
The 30-year-old admits to frustration over his time at Preston and would welcome a move to Hibs.
Hart said in the Sunday Mail: "I was closing to leaving before Darren came in - either on loan or a transfer. Hibs were there or thereabouts and the deal was almost done the morning Alan got sacked."
Hart, who joined Preston two-and-a-half years ago, added: "At Aberdeen, I played every week and I need that again to prove my worth. But I have a decent contract at Preston and I'm 30 now.
"So I'm not going to walk away from it unless I have something else on similar terms."
Hart has not given up hope of resurrecting his career at Deepdale, saying: "I'll see if I can change the gaffer's mind in training and maybe come off the transfer list.
"But if I'm going to sit in the reserves I'd rather move on. Until I get the release papers, though, I'm not pushing for anything.
"Hibs are the ones who have shown an interest but I've not spoken in depth with them. They're a great club and John Hughes is a great manager. So if that came about then great."