Harte has enjoyed a great season with Carlisle United, scoring 18 goals from defence and earning a place in the League One PFA Team of the Year.
Carlisle have offered the left-back a new deal at Brunton Park as they look to ward off interested parties, but as yet no contract has been agreed.
A number of clubs are thought to be monitoring Harte's situation at Carlisle, with the likes of Watford, Norwich and Queens Park Rangers all admirers of the full-back.
However, Leeds are ready to steal a march on their rivals by making a move for the Republic of Ireland ace.
Harte could be tempted by a move away from Carlisle with the opportunity of plying his trade at a higher level than League One.