Preston North End knocked back after checking loan availability of Burnley's three England goalkeepers
The Lilywhites asked whether Hart, Nick Pope or Tom Heaton were available on loan for the rest of the season but the answer was no.
They are now looking at other targets and are hoping to complete a permanent signing in the next few days.
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Hide AdBurnley are well stocked for keepers and North End were linked with Heaton last month.
Heaton has since regained his first-team, starting the Clarets' last two Premier League games, both of which they won.
Against Barnsley in the FA Cup last Saturday, Pope started - he's recently returned to fitness after a shoulder injury sustained in their Europa League tie with Aberdeen at the start of the campaign.
Hart, who won 75 caps for England, played in Burnley's first 19 Premier League games.
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Hide AdNorth End have loaned out Chris Maxwell to Charlton Athletic for the remainder of the season, leaving them in the market for another keeper.
Declan Rudd has been first-choice since regaining his place from Maxwell in November, while Michael Crowe played in the FA Cup defeat to Doncaster Rovers.
Another of the club's keepers, Mathew Hudson, recently returned from a loan spell with Bury.