The Evening News has learned that talks are moving in a positive direction between Damour and Hearts after the two clubs agreed a season-long loan.
The 28-year-old is receptive to moving to Scotland and the finer details of the move are now being negotiated. That may include an option for Hearts to sign Damour permanently next summer if he agrees terms.
The Edinburgh club remain hopeful of signing another midfielder in the shape of Republic of Ireland internationalist Glenn Whelan. The 35-year-old has been mulling over a proposed one-year contract but must decide whether to leave his family, who are based in England.
As things stand, a deal for Damour is more likely to happen first. Hearts officials are working to try to complete negotiations ahead of Saturday's Premiership match against Ross County at Tynecastle Park.