Arsenal and Liverpool have been alerted in signing Bernard after the Shakhtar Donetsk star hinted that he could leave the Ukrainian club in the summer transfer window.
The Daily Mirror claims that the Brazilian international is unhappy amid the ongoing civil unrest in Ukraine and is eyeing a switch to the Premier League.
Bernard signed a five-year deal with Shakhtar from the Brazilian outfit Atletico Mineiro in 2013, despite strong interest from Tottenham Hotspur last summer.
Bernard also seems to be unhappy about the number of regular first-team opportunities that is being handed to him by manager Mircea Lucescu. The winger has started in only 14 matches in all competitions for the reigning Ukrainian champions and has hinted at considering his future with Shakhtar once the World Cup concludes.
"I can't talk about what's going on in Ukraine as I was told not to do so, but I have gone through everything there and so did my parents, as they were with me. It's complicated," Sky Sports quoted Bernard as saying.
"As for the future, I can't say anything. There is a large turnover of players that pleases no-one in the squad. I was used to playing on Wednesdays and Sundays here [in Brazil] while at Shakhtar I have played only 25 games so far."
"It's hard and complicated to be in a country where I barely play, I hope that this will change. I leave my future after the World Cup in God's hands," he concluded.
Earlier this month, Bernard had revealed that although there was interest from English sides, the Gunners were unable to afford the fee necessary for acquiring his services immediately.
The 21-year-old is currently on national team duty for the World Cup in his home country, after being named in the 23-man squad by Brazil manager Luiz Felipe Scolari.
The Mirror's report also suggests that Shakhtar could be tempted to sell Bernard if his potential suitors are willing to shell out £19m.
Both Arsenal and Liverpool are looking to splash the cash and make quality signings in the upcoming transfer window to bolster their prospects of winning silverware in the next season.