With Jose Mourinho involved in constant power struggles at the Santiago Bernabeu, and having had individual spats with a number of players - most notably club captain Iker Casillas - the Portuguese coach is expected to be replaced at the end of the season.
Wenger has rejected overtures from Real Madrid in the past, committing himself to the Gunners project he is working on at the Emirates Stadium.
However, Mourinho's possible departure from the Spanish capital, could pave way for another offer for the Arsenal boss to consider.
Paris Saint-Germain head coach Carlo Ancelotti is also in the frame to take over at Los Blancos, according to Spanish newspaper El Confidencial, with the fact the Italian tactician has a Spanish wife a possible reason he might favour Madrid over Paris.
Wenger remains the number one choice, though, with Real Madrid officials ready to end the Frenchman's 16-year stay in north London, and tempt him into one final challenge in La Liga.