The 21-year-old Brazilian only joined the Eastern European giants in a £20m switch over the summer, but has been unable to establish himself as a key first-team player.
Spurs were one of a host of clubs linked with the silky playmaker prior to his switch to the Ukrainian side, and have since remained interested.
Tim Sherwood is desperate to add to his squad in the coming weeks, after inheriting his current crop of players from Andre Villas-Boas.
Although he has a talented unit at his disposal, the new White Hart Lane chief is keen to add stars that suit his playing style, with Bernard among the list of names on his radar.
It is understood that contact between Tottenham and Shakhtar has been made, after the player’s agent touted his client around in a bid to secure regular playing time ahead of the World Cup.
It’s likely that significant loan fee will have to be paid to push through a deal, but the Londoners could offset this by selling Etienne Capoue to Napoli for around £7m.