The former Celtic boss, who exited Parkhead at the end of October, is said to be close to taking over at Al Qadsiah in the Saudi Pro League.
The club currently sit fifth in the table and feature former Real Madrid defender Nacho Fernandez and Belgium goalkeeper Koen Casteels.
Al Qadsiah are keen to sign Salah, claims talkSPORT, with the Egyptian winger's future at Liverpool uncertain following an interview where he claimed the club had 'threw him under the bus'.
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This potential signing could lead to Rodgers managing Salah in a striking twist.
Rodgers will also reunite with a familiar face in the Middle East, as former Rangers CEO James Bisgrove is part of the Al Qadsiah setup.
John Kennedy, who spent more than 25 years with the William Hill Premiership champions as a player, scout, and coach, has reportedly agreed to join Al Qadsiah, too.
The club dismissed their Spanish head coach, Michel Gonzalez, after a penalty shootout defeat to Al Ahli in the King's Cup quarter-finals at the weekend.