Speaking after his side's 1-1 draw at Newcastle, Wenger said: "I will give him my opinion, which I do not hide. I have said that many times.
"I think it has to be an Englishman because it is English football and the English football federation.
"You know what makes me sad? I am more nationalistic than you because you want to go for (Jose) Mourinho, for (Fabio) Capello - I am the only one who goes for an Englishman."
Asked whom he might recommend specifically, Wenger, who had earlier jokingly cited doctors' confidentiality over any talks with the FA, said: "I don't tell you, that's the confidentiality clause again."