The 43-year-old met Ann Budge, owner of the Edinburgh club, and director of football Craig Levein. He is one of the first to be formally interviewed for a job which became vacant when Hearts sacked Ian Cathro last week.
Others will also be approached in the coming days, with the former England manager Steve McClaren also on the shortlist to replace Cathro. Pressley’s interview comes a year since his last managerial job at English League One club Fleetwood Town.
He previously said he would have no interest in returning to Scotland to manage but the chance to take the reins at Hearts would guarantee a rethink. Pressley spent eight years at Tynecastle as a player and captained the club to their 2006 Scottish Cup success.
His managerial CV includes spells in charge of Falkirk, Coventry City and Fleetwood. He most recently helped out at the Strachan Football Foundation, run by Scotland manager Gordon Strachan.
Hearts are in no rush to make an appointment and will head to Rugby Park to face Kilmarnock this weekend with Jon Daly in interim charge. He is still expected to be in place the following week against Rangers whilst the Tynecastle hierarchy decide who is the man to take them forward.