The Serie A club wrap up their season with a home game against Lazio on Sunday, but the former Liverpool boss could be set to announce his impending departure for the Bernabeu three days before that.
A statement published on Napoli’s official website reads: “President Aurelio De Laurentiis announced this afternoon that in a few hours??? time there would be some news.
“That news is that at 1pm (local time) on Thursday, there will be a press conference held by the club president, alongside Rafa Benitez.”
Benitez has already been described as being “99 per cent” certain to be the next Real coach following the sacking of Carlo Ancelotti on Monday.
Ancelotti’s representative Ernesto Bronzetti fully expects the 55-year-old, who started his managerial career with Real’s reserve side, to become the club’s 13th coach since 2003.
He told Italian television channel Rai Sport: “Benitez is 99 per cent sure to go to Real.”
Ancelotti’s departure had been anticipated since Real were knocked out of the Champions League semi-finals by Juventus earlier this month.
The former Chelsea and Paris St Germain boss won the Champions League and Copa del Rey in his first season in charge at the Bernabeu and also helped Real lift the UEFA Super Cup and FIFA Club World Cup in 2014.
However, Real could not add any more trophies this year as they finished second to Barcelona in La Liga as well as being knocked out of Europe and the Copa del Rey.
Aside from Benitez, the likes of Jurgen Klopp and Unai Emery have been linked with the Real post.
Madrid-born Benitez has previously spoken of his wish to manage Los Blancos, calling the club his “sweetheart” while he was in interim charge of Chelsea in 2013.
Perez said in a press conference on Monday night to announce Ancelotti’s departure: “Next week, we will know the name of the new manager of Real Madrid.
“With our great team, talent and hard work, we will be able to give satisfaction and happiness to our fans and our members.
“I want to publicly say thank you to Carlo Ancelotti for these two years, for his hard work and all his affection, and tell him this is still his house and his home.”
Perez added: “It was a very difficult decision to make; the demands at this club are the utmost because Madrid always wants to win silverware.
“The affection that the players and the fans have for Carlo is the same as the affection I myself have for him.
“What did Ancelotti do wrong? I don’t know. The demands here at Real Madrid are very high.”