The Daily Mail says Real Madrid head coach Manuel Pellegrini and AC Milan's Leonardo have both been told they must do better after defeats in Europe this week - and both are said to see Benitez as the man who could transform their fortunes.
Juventus also remain in the frame, with current coach Alberto Zaccheroni only contracted until June.
Reports in Spain suggest Pellegrini could be sacked if Madrid go out of the Champions League next month.
The Bernabeu giants were beaten 1-0 at Lyon on Tuesday night and Madrid's director general Jorge Valdano is said to have warned the Chilean that an exit at the last 16 stage will not be tolerated.
Pellegrini came under fire before Christmas when his team of Galacticos were knocked out of the Spanish Cup by lowly Alcorcon, but his side are just two points off leaders Barcelona in the hunt for La Liga.