The English Premier League side are interested in the 20-year-old star, and the Brazil Serie A outfit want £22million for the winger.
Bernard's father Delio Duarte said there was interest in Bernard, while his countryman Hulk has told him to move to Porto.
"Nothing is decided yet but we know there is interest from Arsenal. However, there has been nothing official from them," Duarte told O Jogo.
"Hulk has convinced Bernard that Porto would be better for him at this stage of his career."
Bernard led Mineiro to Copa Libertadores glory on Wednesday but looks almost certain to leave the club.
Arsenal, who are also interested in signing Liverpool star Luis Suarez, may be waiting to offload attacker Gervinho to Roma before going after Bernard.
But the delay in that move has allowed Porto to move into pole position to sign Bernard, a move Duarte would be happy with.
Reports in Italy suggest Roma are close to finalising the £7million signing of Ivory Coast international Gervinho.
