The 31-year-old midfielder has held detailed talks with lower league clubs in his homeland, including FC Versailles, and is on the verge of securing a permanent transfer from Edinburgh.
Damour still has one year remaining on the four-year Hearts contract he signed in 2019, but that will be cancelled to let him move on. He is due to be released after spending last season on loan at Le Mans in the third tier of French football.
Hearts agreed to that loan move on the understanding they would save around £100,000 in wages during the coming season when Damour moved on permanently. He is one of the highest earners at Tynecastle Park but has not made a competitive appearance in Scotland since March 2020.
He featured briefly during pre-season friendy matches last summer before finalising the season-long loan with Le Mans. The French third division side could not contribute much money towards his salary due to their lower-league status so a permanent exit is now on the cards.
Versailles have been promoted to the same league – the Championnat National – and are hopeful of finalising Damour’s capture in the coming days as part of an ambitious recruitment drive.
Damour was initially brought to Tynecastle from Cardiff City by former Hearts manager Craig Levein. He fell out of favour and his departure will free up cash for current manager, Robbie Neilson, to continue strengthening his squad ahead of the new campaign.
Winger Alan Forrest plus defenders Kye Rowles and Lewis Neilson have already been signed.