According to UOL Esporte in Brazil, Arsenal and Liverpool both asked about potentially signing Bernard on a free transfer, but chose not to make him a concrete offer.
Bernard, 25, became one of the biggest talents in Brazil during his time with Atletico Mineiro, as clubs around the world were battling for his signature in the summer of 2013 after 22 goals in 100 games.
The diminutive playmaker chose a move to Shakhtar Donetsk, in the hope of following in the footsteps of players like Elano, Fernandinho, Willian and Douglas Costa in becoming Brazilian sensations with the Ukrainian giants.
During his time at the Donbass Arena, Bernard has notched 28 goals in 157 games, with his best return coming last season having found the net 10 times as well as four assists before allowing his contract to expire.
Bernard will be assessing his options, and UOL Esporte in Brazil report that Arsenal and Liverpool both enquired about a deal for the free agent, but they didn't follow up with a concrete offer.
It's claimed that Bernard was hoping for a better offer, possibly from a club like Arsenal or Liverpool, but may now have to scale back his expectations in order to find a club this summer, but he could come back to haunt the two Premier League giants with West Ham if he decides on a move to East London.