Cavani, 33, is surprisingly still without a club after leaving Paris Saint-Germain at the end of his contract.
Links with Juventus, Roma, Benfica, Atletico Madrid and others have not resulted in the Uruguayan finding a new team.
It is reported that Cavani was pitched to Real Madrid prior to their match against Real Sociedad on Sunday.
While Cavani would not command a transfer fee, his salary demands (around €7m) are something Madrid have to consider.
Madrid would welcome the signing of an expert striker, particularly after drawing a blank in their 0-0 draw with Sociedad.
As a result, Cavani has not been ruled out and Los Blancos are taking some time to consider it.
In the meantime, Cavani is training hard on his farm in Uruguay while waiting for a decision on his future.