According to reports, Uefa, with the help of several high-profile football figures, is trying to persuade Wenger to run as a rival to scandal-plagued Gianni Infantino in the election for a new president in March.
The 77-year-old is expected to make a decision this week. Candidates must register by November 18.
Japan's Kozo Tashima, who sits on the FIFA board, has also announced that he wants to run.
Wenger has been FIFA's head of global football development since 2019, when Infantino recruited him. His contract expires at the end of the year.
The Frenchman managed Arsenal from 1996 to 2018 and won three Premier League titles, among other honours.
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