That is the stunning revelation coming out of France today, with former PSG president Charles Villeneuve revealing the meeting.
Wenger quit Arsenal last summer after 22 years as manager.
The Frenchman went through a number of tricky periods during his tenure as Gunners boss.
But he always remained loyal to the Arsenal project – even when fans were on his back and the board would not support him in the transfer market.
Now, it has emerged that Wenger spoke to Real during his Arsenal tenure over the possibility of moving to the Bernabeu.
The meeting happened in a gyn in Italy, with former PSG president Villeneuve also in the room.
“Two clubs have always wanted him as a coach, and I attended a gym in Italy at the Real Madrid negotiations with him,” Villeneuve told Paris United.
“But he decided to stay at Arsenal.”
Villeneuve, a friend of Wenger’s, did not specify when the meeting took place.
Real went though 18 managers while Wenger was at Arsenal, including appointing Fabio Capello twice during that reign.
Some of Wenger’s greatest adversaries in football – including Jose Mourinho, Manuel Pellegrini and Carlo Ancelotti – have taken up the Real post.
Wenger is now out of work and seeking a new post, insisting he is keen to get into management after Christmas.
The Real job was recently available after the Bernabeu club sacked Julen Lopetegui.
But Santiago Solari has been placed in charge, as Real failed to lure Antonio Conte to Spain.
There are reports Wenger could end up back at his former club Monaco, where Thierry Henry is currently struggling to prise the principality club out of a dire run of form.
Henry only joined Monaco in October but has failed to oversee a single victory so far.