The Cottagers axed Slavisa Jokanovic on Wednesday before immediately putting former Leicester and Chelsea boss Ranieri in place.
But The Mirror claims Wenger was the club’s first choice.
Owner Shahid Khan admitted they had sounded out a number of candidates before eventually appointing the Italian.
Wenger is said to be one of those people but it is claimed he does not want to manage another Premier League club out of respect to former club Arsenal.
Khan is understood to be close to Arsenal owner Stan Kroenke because of their NFL connections.
But Wenger could be holding out for a top job in Europe and has been linked with the post at AC Milan if current boss Gennaro Gattuso is sacked.
Ex-Arsenal chief executive Ivan Gazidis is set to take a similar role with the Italian giants in December.
And he is said to be keen on a reunion with Wenger as Gattuso has overseen a difficult start to the season.
Wenger’s decision to turn down the offer from Fulham gave Ranieri the chance to return to English football for the first time since being sacked by Leicester in February last year.
And he says he is delighted to be handed the opportunity at Craven Cottage.
“It is an honour to accept Mr. Khan’s invitation and opportunity to lead Fulham, a fantastic club with tradition and history,” he said.
“The objective at Fulham should never be to merely survive in the Premier League. We must at all times be a difficult opponent and should expect to succeed.
“This Fulham squad has exceptional talent that is contrary to its position in the table.
“I know this team is very capable of better performances, which we will work on straight away as we prepare for Southampton at the Cottage.”
Ranieri’s first game in charge will see bottom-of-the-table Fulham take on fellow strugglers Southampton at home on November 24.
Khan claims appointing Ranieri comes without risk despite the fact he struggled in his final season with Leicester.
The 67-year-old guided Leicester to a shock Premier League title in 2015-16 but was sacked by the Foxes after 25 games of the following campaign with the club languishing in 17th in the table.
His last job was as manager of Nantes but he was sacked after just one season with the Ligue 1 club.
And while Khan was reluctant to let Jovanovic – who guided them to promotion last season – go, he is delighted to have attracted someone with Ranieri’s experience.
“I wasn’t anticipating having to make this announcement related to Slavisa and wish the circumstances were such that I didn’t have to,” he said.
“But our path this season has led me to make what I know is the correct decision, at the right time, for our players, the Club and our supporters,”
“Slavisa will always have my appreciation and respect for everything he did to return Fulham to top-flight football.
“I am hoping everyone in the Fulham Family shares my heartfelt sentiments for Slavisa and joins me in wishing him success and good fortune, wherever his next stop may be.”
He added: “Making a change without having the right answer or succession plan was not an option, so having someone of Claudio’s calibre ready to accept our challenge was comforting but, most of all, essential.
“Claudio is risk-free and ready-made for the Premier League, and particularly so for what we need at this moment at Fulham.
“His recent body of work with Leicester City is literally legendary, and then you look at Claudio’s experience with Chelsea and big clubs throughout Europe, and it’s pretty evident we are welcoming an extraordinary football man to Fulham Football Club.”