It is believed the club made a £4.5 million offer for the 27-year-old but Porto president Pinto Da Costa turned it down as they value McCarthy at £6 million.
Porto coach Co Adriaanse is reported to have said, “We are not interested in the operation.
“I need Benni's work and goals and I am not interested in him leaving.”
Alan Pardew now has to decide whether to increase his offer McCarthy or turn his attentions again to Monaco’s Emmanuel Adebayor now the French side have failed to qualify for the lucrative Champions League group stages. He is also believed to be weighing up a move for Portuguese star Nuno Gomes.