Benzema and Messi reportedly set for moves to Saudi Arabia
Saudi state television channel Al-Ekhbariya claimed 35-year-old Benzema had signed with Jeddah-based Al-Ittihad.
Senior officials from Al Hilal have flown to France to try and seal a deal for Messi after the 35-year-old played his last game for Paris Saint-Germain on Saturday.
The Saudi delegation plans to meet Messi's father and agent, Jorge, with the aiming of completing the signing as soon as possible, sources told AFP on Sunday.
Messi arrived in Paris two seasons ago from Barcelona but was unable to help PSG win an elusive Champions League title, as the club suffered last-16 defeats in both campaigns with the Argentine maestro.
Benzema and Messi are in line to join Cristiano Ronaldo in the Gulf kingdom after the Portugal attacker moved to Al Nassr from Manchester United following last year's World Cup.
According to Al-Ekhbariya, the president of Saudi champions Al-Ittihad and his deputy were in the Spanish capital "to officially sign" Benzema in a "record transfer with Real Madrid".
The broadcaster said Benzema had agreed a two-year deal with the club, based on the Red Sea shores of the Gulf kingdom.
Benzema scored a penalty in his final Madrid game as they drew 1-1 with Athletic Bilbao on Sunday.
Over the past week, Madrid boss Carlo Ancelotti - as well as Benzema himself - had said the striker would not leave his contract at Santiago Bernabeu early, with one year left of it to run.
Benzema lifted five Champions Leagues, four La Liga titles and three Copas del Rey with Madrid and is the holder of the Ballon d'Or for the world's best player.
Leaving Lyon
Benzema joined Madrid in 2009 from Ligue 1 side and hometown outfit Lyon.
Benzema established himself as a key player alongside Ronaldo and Gareth Bale in the vaunted "BBC" attacking trident, before developing into the team's leader when the Portugal striker left in 2018.
He is Real Madrid's second top scorer of all-time, with 354 goals for the Spaniard, behind only Ronaldo on 450.
Benzema battled with Gonzalo Higuain for a regular starting spot in his early days at Madrid, and was once derided by then-coach Jose Mourinho for being a "cat" instead of the "hunting dog" he wanted.
While playing alongside Ronaldo, Benzema took the role of supplier and worked hard to provide for his teammate.
The forward greatly increased his goal output after Ronaldo left, playing centrally, and scored 44 in 46 games last season, a performance that earned him the 2022 Ballon d'Or.
Benzema's most recent conquest was the Copa del Rey in May, with Real Madrid beating Osasuna to lift the title for the first time since 2014.
Benzema may cherish last season's Champions League triumph the most of all his successes because he played a crucial role in winning it.
The forward scored a stunning hat-trick to help Madrid come from behind against Paris Saint-Germain in the last 16 and progress.
Benzema netted another treble at Stamford Bridge in the quarter-finals against Chelsea and scored the extra-time goal in the second leg which sent his team into the semi-finals.
The forward also scored three goals over two games against Pep Guardiola's Manchester City to help Madrid reach the final, which they won against Liverpool in Paris - his first Champions League triumph as the team's figurehead.
