Former Aberdeen defender Hart came close to joining the Edinburgh side 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. However, he is prepared to sit out the final year of his contract if he is unable to agree a similar deal elsewhere.
Hart said yesterday: "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."
Meanwhile, a Sunday newspaper report yesterday claimed that Hibs striker Anthony Stokes is a target for Celtic.
The Parkhead club, who are expected to confirm this week that interim manager Neil Lennon will be handed the role permanently, are said to be lining up a bid for the Easter Road outfit's top goalscorer.
The Republic of Ireland international, 21, scored 23 goals in an impressive first season for Hughes' side – including goals in both of Hibs' SPL matches at Celtic Park – and is reported to have impressed Lennon.
Stokes had an opportunity to join Celtic earlier in his career but spurned the chance, to join Sunderland instead.
Hibs, who netted more than 500,000 in a sell-on clause when former forward Steven Fletcher joined Wolves from Burnley last week, may not be in a hurry to sell one of their prize assets however. Stokes is under contract to 2012, and only a fee of 2m-plus might tempt Hibs to even consider selling.