The ex-Denmark international, who spent about five years at Old Trafford in the mid-to-late 1980s, spent one season working alongside Dutchman John van 't Schip with the expansion club but will no longer continue in his role.
Heart CEO Scott Munn said that the 50-year old was keen to spend more time with his family but was pleased to add that Olsen may take up a part-time position with the sophomore club.
"Jesper may well stay on working a couple of days a week in a mentoring role but he has told us he doesn't want to work and travel with the team through the course of a long season on a full-time basis," Munn told The World Game.
"In a financial sense he doesn't need to do that and he would like to spend more time with his family in future. He was with us for the love of the game, not because he needed the money."