The 24-year-old, along with ex-Motherwell striker Louis Moult has not been offered the chance to remain with the Championship side upon the expiration of his contract.
Tynecastle boss Robbie Neilson said late last month the player is keen to return to Edinburgh for a permanent stay and talks were already underway.
An impressive performer and fans favourite when he was fit enough to play, Ginnelly was limited to only ten matches across the entire season as he dealt with various injury issues.
His final match came in January’s 4-0 win over Raith Rovers where he lasted just 16 minutes before being forced off.
His most noted contribution came as a substitute in the Scottish Cup final lossss to Celtic. Ginnelly’s speed in attack helped Hearts get back into the match before he netted to tie the game up for a second time in extra-time.