The north London duo were linked with Bernard before the youngster completed his move to Ukraine last summer for £20m.
Despite losing out to Shakhtar at the time, Tottenham and Arsenal may get another opportunity sooner than they expected.
The Daily Express report claims Bernard may seek a move away from Shakhtar following the recent turmoil in Ukraine - something the player has confirmed.
"The demonstrations in the city centre, in front of city hall, have already begun," said Bernard.
"My parents and a cousin live with me. I have already talked to the ambassador of Brazil about if it gets worst if we leave Ukraine as soon as possible.
"You cannot stay quiet. I have this concern but it is now left in the hands of God."
But while Bernard says he still dreams of playing for a major European club at some point in his career, he believes the fact Shakhtar paid such a large fee for him recently may make it difficult for him to leave in the short term.
"I have the dream of playing for a big European club but I have only been at this club for seven months," he continued. "It is a big investment and the president does not want to release me."
The 21-year-old winger is expected to feature for Brazil in the World Cup this summer after playing a limited role in their Confederations Cup triumph last year.
He moved to Shakhtar, a popular destination for Brazilians on their first stop in European football, from Atletico Mineiro, where he played alongside Ronaldinho.
Donetsk is in the eastern part of Ukraine, a predominately Russian-speaking area that has seen protests in the wake of Viktor Yanukovych's flight from power in the country.