The former Roma and Shakhtar Donetsk boss was the early frontrunner after holding discussions not long after Steve Bruce was relieved of his duties.
However, the interest in Fonseca was paused as Amanda Staveley & Co turned their attention to other candidates such as Unai Emery, Roberto Martinez and Eddie Howe.
That hasn’t put the 48-year-old off though, and according to Sky Sports, he remains interested in taking charge at St James’s Park.
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Newcastle’s owners had hoped to have a new manager in place in time for Saturday’s clash at Brighton and Hove Albion but Emery’s rejection may have delayed proceedings.
The former Arsenal boss was the leading candidate but confirmed in a statement on Wednesday that he intended to stay at Villarreal.
The Magpies are 19th in the Premier League, without a win in 10 matches and six points from safety.