The 26-year-old forward is available for transfer following once season in the Belgian top flight with Beershot.
He was signed for close to £1million last summer by the Belgians, but both player and club have had an underwhelming campaign.
The Evening News reports that talks have progressed towards an agreement for the Scotland international striker to move to Tynecastle Park. Money is now being discussed as the two clubs look to tie up a deal.
Hearts had been quoted a £500,000 transfer fee for Shankland, who moved to Belgium from Dundee United in a £1m deal last August, but Beerschot would be willing to accept a lower initial payment with the remainder made up in performance-related add-ons.
Shankland played for current Hearts manager Robbie Neilson at Dundee United when he brought him in from Ayr United, scoring 28 goals in 33 games to help Dundee United win the 2019-20 Championship title.
Shankland dropped out of the Scotland squad prior to last summer's European Championship and did not make Steve Clarke's final 26-man cut for the tournament. The last of his four international caps came away against Slovakia in a Nations League tie in November 2020.
Hearts have already signed defenders Kye Rowles and Lewis Neilson from Central Coast Mariners and Dundee United respectively, plus winger Alan Forrest on a free transfer from Livingston.
The Tynecastle club are expected to bolster their squad further given that they have guaranteed European football up until Christmas after finishing third in the cinch Premiership last season.