The 21-year-old midfielder was touted as a target for both the Gunners and their north London rivals Tottenham last summer before he opted to move to Ukraine.
Premier League champions City are believed to have entered the race for the Brazil international after the forward impressed at Shakhtar Donetsk following his £30m move.
Whilst Bernard revealed that his representatives are attempting to sort his future, the South American star refused to give any update on a potential move to the Premier League in the summer transfer window.
“I made it clear since I arrived [to join the national team] that I won’t comment about the possibility of a transfer as I am focused on the World Cup,” Bernard told Superesportes.
“It’s a unique moment in the career of a player, I want to mature and learn a lot here with my more experienced team-mates.
“I leave my off the field situation to be handled by those who have the right to do so without me.
“I don’t know [what will happen] after the World Cup, I have people to handle the off the field things.”
Bernard scored two goals in 17 appearances in Ukraine’s Premier League.