The 77-year-old, who currently serves as FIFA's director of global football development, has been approached by figures hoping to persuade him to stand against the incumbent when the organisation elects its next president on March 18, 2027, in Rabat, Morocco.
According to L'Équipe, Wenger has not yet made a final decision, but is now closer to entering the contest after a prolonged period of hesitation. Several meetings are planned in the coming days, with an announcement expected around the middle of next week.
Those seeking an alternative to Infantino believe Wenger would bring considerable advantages to the campaign. His international reputation, decades of experience in football and standing across the global game make him an attractive potential candidate.
His relationships in Africa and Asia are viewed as particularly valuable, while the fact that he has no association with UEFA could help reassure national federations outside Europe that his candidacy would not simply represent a European challenge to Infantino.
There is also reported support for Wenger from within FIFA itself, with some figures in the organisation encouraging him to enter the race.
His age would, however, limit the length of any potential presidency. If elected, Wenger would be eligible to serve only one four-year term.
Infantino is seeking another mandate despite growing criticism of his leadership and a series of controversies surrounding FIFA. The possibility of Wenger standing would give those seeking a change at the top of the organisation a candidate with an unusually high profile in the football world.
Wenger would not be the only potential challenger. Kozo Tashima, honorary president of the Japan Football Association, has already announced his intention to stand.
The former Arsenal manager has yet to confirm whether he will follow that route. His decision is expected to become clearer next week, as those seeking to convince him make their final case.
For now, the prospect of a Wenger candidacy remains unconfirmed, but the possibility of one of football's most recognisable figures challenging Infantino has become a serious talking point ahead of the election.