The Cottagers sacked Slavisa Jokanovic on Wednesday, with the club bottom of the Premier League, and immediately appointed former Chelsea and Leicester City manager Ranieri as his replacement.
It is understood the Italian was Fulham’s first-choice to become their new manager, and was the only candidate they offered the job too.
However, the club admitted they spoke to various candidates while Jokanovic was still in charge, and it is understood Wenger was one of them.
The former Arsenal boss has been out of work since leaving the Emirates in the summer following 22 years with the north London club.
Wenger won three Premier League titles and seven FA Cups during his time with the Gunners, and his appointment would have been a major coup for Fulham, who were only promoted last season and have just five points from 12 matches this campaign.
Wenger was not offered the job at Craven Cottage, though, having made it clear he was not interested in entering into formal discussions.
The 69-year-old told Sky Sports News last month he is preparing to return to football at the start of next year, but that he would find it “odd” to coach another English side.
As well as Wenger, Sky sources understand several other out of work managers were spoken to by Fulham while they considered the candidates to replace Jokanovic.
Former Chelsea and Tottenham manager Andre Villas-Boas and one-time Watford manager Quique Sanchez Flores were both sounded out by Fulham before they decided to go with Ranieri.