The Queens Park Rangers goalkeeper has attracted shock interest from a number of top European clubs, with the Spanish giants the latest side believed to be courting his signature.
Earlier this week, The Sun reported that Red Devils boss Sir Alex Ferguson was considering a bid to bring Cesar to Old Trafford as a short-term replacement for troubled number one, David De Gea.
The same exclusive suggested that Arsenal were losing faith in Wojciech Szczesny, and as a result Arsene Wenger was looking at the 33-year-old Brazilian as a future custodian for the Gunners at the Emirates Stadium.
However, both Premier League clubs could now face further competition from Real Madrid, with Jose Mourinho on the lookout for an emergency signing, after Iker Casillas was ruled out for up to two months with a broken hand.
Cesar played under Mourinho at Inter Milan and is on Real Madrid's short-list to replace Casillas as they prepare for a two-leg Champions League last-16 showdown with Manchester United next month.
A move to the Spanish capital would be an incredible jump from the Premier League's bottom club to the reigning Primera Division champions, but Cesar - who is on £70,000 a week at Loftus Road - was once rated as among the best in the world at his position.
The South American stopper won five Serie A titles and the Champions League during his seven-year stay at the San Siro, before signing a four-year deal with QPR in the summer.