The club's president Florentino Perez called the Frenchman say Paris United but there is no suggestion of a formal offer.
Lopetegui was sacked last week with Santiago Solari placed in interim charge – Mauricio Pochettino is the club's first choice as a replacement.
But as SunSport exclusively revealed, the Tottenham boss has rejected their advances amid behind-the-scenes disruption at the Bernabeu.
It means Solari is the favourite to be the next permanent manager as the club have just a week left to secure an appointment due to Spanish FA regulations.
Antonio Conte and Roberto Martinez were linked with the post but are understood to be out of the running while Wenger could prove to be a shock appointment.
According to the same outlet, Wenger – who left the Emirates in May – has also been sounded out by world governing body Fifa to assume a role there.
The former Arsenal boss, 69, was last night linked to the managerial job at AC Milan.
Gennaro Gattuso is under pressure and at risk of losing his job despite winning six of his last eight games in charge.
Billionaire businessman Paul Singer took control of Milan in June and has already recruited ex-Gunners chief executive Ivan Gazidis to take up a similar role at the San Siro.
Singer, who has spent a lot time in London watching Premier League football, is a big fan of Wenger and has reportedly given the green light to Gazidis to make contact with the French coach.
But the Frenchman has also been lined up by Paris Saint-Germain, who are understood to want to recruit him as sporting director.
Manager Thomas Tuchel and current sporting director Antero Henrique have been at loggerheads in recent weeks despite the French side's perfect start to the Ligue 1 season.
It means Wenger is in high demand and is sure to be back in the game in the coming months.
He recently revealed to Sky Sports he is missing the day-to-day involvement after 22 years at Arsenal and was sure of a return next year.
The 69-year-old said: "I'll be somewhere early next year but I do not know where, I got a good rest. I watched a lot of football, I miss it."
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