The Sun says Preston are looking for a new goalkeeper and have asked their neighbours if they can have the out of favour Hart, who only joined Burnley at the start of this season.
He would be getting regular football in the Championship with Preston, though. They have just let Chris Maxwell go to Charlton on loan.
"It makes sense to move to a bigger club!!" joked Preston fan and former England cricket captain Andrew Flintoff on Twitter. "Come on Joe you know it makes sense."