Former Aberdeen defender Hart came close to joining Hibs in January before Alan Irvine was replaced as North End manager by Darren Ferguson.
Hart, who had been frozen out under Irvine, then found himself back in the side, only to be axed again and placed on the transfer list.
The 30-year-old admits to frustration over his time at Preston and would welcome a move to Hibs.
But he is prepared to sit out the final year of his contract if he is unable to agree a similar deal elsewhere.
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."
Source: Team Talk
Source: Team Talk