"At the moment I have not made any offer for Anelka," the Arsenal manager said.
"I felt we had the strikers we needed, and also I wanted a player like Eduardo, who can play on the flanks and with (Emmanuel) Adebayor, or with (Robin) van Persie.
"That is why we have gone for Eduardo, and it was more a question of choice rather than the quality of Anelka, because I rate him very highly.
"It was just we have others who play in the same position."
Wenger added: "I can bring in who I want and the board do not interfere in that, unless there is a compulsory financial situation that we cannot afford."