The Brazil international has spent the past four-and-a-half years plying his trade with the Ukrainian giants after joining them from Atletico Mineiro.
But his time at the club looks set to come to an end with a stalemate ensuing in contract negotiations.
Bernard is unwilling to commit his future to Shakhtar, with his current deal due to expire at the end of June 2018.
And the latest reports suggest that situation means he has had an £8.7m (€10m) price tag slapped on him.
Transfer Market Web claim Bernard is not short of suitors as the January transfer window draws closer though.
Arsenal are said to have targeted the 25-year-old as they prepare for potential big-name departures.
Alexis Sanchez and Mesut Ozil could quit the Emirates next month and Arsene Wenger is planning ahead.
Arsenal are not alone in wanting to keep Bernard in Europe, with Inter Milan interested in him too.
The Serie A giants’ transfer chief, Walter Sabatini, previously tried to lure the contract rebel to Roma.
Chinese Super League outfit Hebei China Fortune are keen on Bernard as well.
And they may have the resources necessary to blow Arsenal and Inter out of the water if a battle for his signature begins.
Bernard has made 24 appearances in all competitions for Shakhtar this season, scoring nine goals.