The Portuguese side's coach was cagey when asked about a move for the sought-after youngster, while his agent has all but ruled out a deal with the Gunners due the "risk" involved
Arsenal, Liverpool and Tottenham have all been linked with the 20-year-old in recent weeks, but a move to the Premier League has become unlikely after the player's agent, Adriano Spodato, admitted he would like his client to move to Portugal.
But after rumours that Porto would announce a deal before their friendly against Celta on Sunday proved unfounded, Fonseca was keen not to give too much away.
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Spodato had claimed over the weekend that a move to a big European club such as Arsenal would be too risky, and expects things to become clearer in the coming days.
"I can confirm that the possibility [of joining Porto] is strong, but there is Shakhtar, too," he told Mais Futebol. "It should be between those [clubs]. On Monday or Tuesday there should be something more concrete.
"If it was up to me, Bernard would be a Porto player. I told him that this is the best way.
"It is preferable to enter a medium, but good, European club, rather than risk a top club and have no space to play. Indeed, Bernard is very interested in going to Porto."
And Bernard's father, Delio Duarte, also admitted that his son has his heart set on Porto after speaking to compatriot and former Dragao Hulk.
"He wants to continue his career at a club like Porto," Duarte told O Jogo. "He dreams of that. Bernard is Hulk's friend, they became very close in the national squad and they talked about this.
"Hulk spoke highly of the club, and [Bernard] was convinced it would be a safe bet for this stage of his career."