Sergio Ramos, Jordi Alba, Sergio Busquets, N'Golo Kante, Angel Di Maria and Roberto Firmino are also among the seasoned World Cup and Champions League winners being lined up for the Saudi Pro League, the source said.
The latest information comes after Saudi officials flew to Paris and Madrid to try to seal deals with Messi and Benzema respectively, according to sources and reports, that would allow them to join Cristiano Ronaldo in the oil-rich kingdom.
Saudi authorities are "in contact with more than 10 players, many of them won the World Cup or the Champions League, to join the Saudi league next season", the source close to the negotiations said.
In addition to Messi, "the list includes Benzema, Ramos, Di Maria, Modric, Hugo Lloris, Kante, Firmino, Alba and Busquets".
"Beside receiving quite lucrative offers they will play in a very competitive league," the source said, adding that the Saudis aimed to "seal most of the deals" before the new season starts on August 11.
The world's biggest oil exporter has already thrown hundreds of millions at sports deals including Ronaldo's signing, Formula One and the divisive LIV Golf tour, drawing frequent claims it is "sportswashing" its human rights record.
Saudi Arabia, whose neighbour Qatar hosted the World Cup last year, has explored bidding for the competition including a possible tri-continental hosting with Egypt and Greece.
- 'Elevate the Saudi clubs' -
Saudi Arabia's Public Investment Fund, one of the world's biggest sovereign wealth funds, is behind the transfer dealings rather than individual clubs, the sources said.
If the players sign, they will be divided between five Saudi clubs: Al Hilal, Al Nassr, Al Shabab, Al Ittihad and Al Ahly, the sources added.
Separately, a Saudi government official told AFP that the authorities are holding negotiations with "world-class players".
"The objective is to establish a very strong and competitive league and elevate the Saudi clubs' levels," the official said.
All the players listed are major stars at the tail-end of their careers. Firmino is the youngest at 31. Apart from France goalkeeper Lloris, who has a year left at Spurs, all are out of contract this month.
According to the sources, Modric, Ramos, Kante, Alba and Busquets appear the closest to signing.
Modric, Real Madrid's influential midfielder, and Ramos, who is leaving Paris Saint-Germain, would join Ronaldo at Al Nassr, while Kante would play at Saudi champions Al Ittihad, the sources said.
Saudi Arabia, under its 37-year-old de facto ruler, Crown Prince Mohammed bin Salman, is trying to improve its austere image and attract tourists and investment, partly through sport.
While not well known internationally, the Saudi league enjoys a strong following in a country where more than half of the 32 million population -- 51 percent -- is under 30.
The Saudi Pro League is growing to 18 clubs next season, with all teams able to field eight foreign players per match.
Ronaldo, 37, arrived at Al Nassr in January in a two-and-a-half-year deal said to total more than 400 million euros. He has confirmed he will stay at the club next season.
This weekend, Saudi state TV said Benzema, 35, had signed for Al Ittihad. Last month, a source close to the negotiations told AFP that Messi's signing was a "done deal".
"We want people to visit Saudi Arabia to watch football stars," the source added at the time.
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