Reports in the sun claim Miller, currently a free agent, will agree a deal with the Edinburgh side over the next week.
Miller was released by Manager Roy Keane after Sunderlands promotion to the Premiership, however the Hearts management team (whoever they are) clearly feel Miller could do a job in the SPL.
Miller was part of the Sunderland team which went down with only 15 points in the 2005/06 season, a record low for the English Premiership.