The club are looking to respond after title rivals signed and are aiming to agree a deal worth €45million (£40m) in the coming days.
Ancelotti was a firm advocate of Benzema during his time as Real Madrid manager and believes he will add a touch of stardust as well as quality to his Napoli squad.
Benzema has been a consistent performer since arriving at the Bernabeu in 2009 and has scored 192 goals in 413 appearances. Despite this, Real Madrid’s fickle fan base have never warmed to him.
Real Madrid president Florentino Perez will be wary of letting another senior member of the squad leave following Ronaldo’s £100m departure to Juventus, and the club would move quickly to secure a replacement.
Valencia striker Rodrigo, who scored 16 goals in La Liga last season, is top of the list to come in, but Real Madrid’s efforts would be firmly on securing Ronaldo’s successor with Chelsea star Eden Hazard leading the shortlist.
The 30-year-old underwent his annual health check-up at the Medical Centre at Real Madrid City and the Sports Medicine Unit of the Sanitas La Moraleja University Hospital.
He then took part in their first training session under new manager Julen Lopetegui, who replaced Zinedine Zidane earlier this summer, as preparations for the new campaign began in earnest.