Al Ahli have already signed Brazilian star Roberto Firmino from Liverpool, Senegal goalkeeper Edouard Mendy from Chelsea and Riyad Mahrez from Manchester City.
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 Brazilian, in his final appearance at Anfield after eight seasons with the Merseyside club, scored in the 89th minute to the delight of the crowd in Liverpool's last home game of the season
Liverpool forward Roberto Firmino expects his final game at Anfield to be an emotional affair and the Brazilian said he is bracing for a flood of tears as he prepares to leave the Premier League club after eight trophy-laden years.
Firmino, whose contract expires in June, has helped Liverpool win the Champions League, Premier League, FA Cup and Club World Cup among other major honours since joining them from Hoffenheim in June 2015.
Liverpool forward Mohamed Salah's struggles in front of goal are down to the club no longer having the "well-drilled" front three that terrorised defences in the past, manager Juergen Klopp said.
Liverpool manager Jurgen Klopp wants Roberto Firmino and James Milner to extend their contracts at Anfield beyond the end of the season.
Liverpool's Roberto Firmino was left off the list Monday as Brazil coach Tite named his World Cup squad, seeking a sixth title with a team led by Neymar and 39-year-old veteran Dani Alves.
Liverpool manager Juergen Klopp hails the ever-present influence of Roberto Firmino after the Brazilian capped an impressive all-round display with two goals in Tuesday's 5-0 Premier League win over Swansea City.