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Salah has been linked with a potential move to Saudi Arabia for a number of seasons, with Al-Ittihad showing a high level of interest in the summer of 2023.
They reportedly saw a nine-figure bid rejected by Liverpool, with Salah ultimately staying on Merseyside after the Reds insisted he was not for sale.
Bilic, who managed Saudi club Al-Fateh until his departure in August, was convinced Salah would join Al-Ittihad at the time because he was said to be unhappy at Liverpool.
The former West Ham boss also suggested that Salah decided to stay at Anfield because he knew that a move to Saudi Arabia would present itself again in the future.
Speaking on The LineUp, via BetMGM and talkSPORT, Bilic said: "There has definitely been a change this season under Arne Slot as, having been in Saudi Arabia last year, I know he wasn’t happy under Jurgen Klopp and we were expecting him to move.
"The whole of Saudi was ready for him and he would have been the star of the league.
Bilic is expecting Salah to complete the switch at some point, insisting that he will almost certainly not sign for another Premier League club given his iconic association with Liverpool.
"He’s the best player in the world now, definitely," added Bilic.
I can’t imagine him at another Premier League club."
Salah is not thinking about life away from Liverpool just yet, though.
Ahead of their Champions League meeting with PSG, he revealed the thought of celebrating another Premier League title was keeping him motivated in spite of his contract situation.
"The biggest motivation is to win the Premier League," he told Optus Sport.
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