Nuno Espirito Santo's side had a £150m bid rejected by the Reds for the 31-year-old Egypt international and reports of a world-record £215m bid were never confirmed.
Several Premier League managers have criticised the fact the Saudi deadline closed almost a week after Europe's major leagues.
How much have Saudi clubs spent?
It was an unprecedented summer of spending by a non-European league, with Saudi Arabia's Public Investment Fund ploughing huge resources into four of their clubs - with other sides also spending big.
Notable Premier League departures to Saudi Arabia
Al-Ittihad: N'Golo Kante (Chelsea), Fabinho (Liverpool)
As well as multiple Premier League stars going to Saudi Arabia for roughly a combined £250m, some of world football's major names will also play in the Gulf.
Paris St-Germain forward Neymar joined Al-Hilal for £77.6m, while Saudi clubs also lured his PSG team-mate Georginio Wijnaldum, Ballon d'Or winner Karim Benzema from Real Madrid, Bayern Munich's Sadio Mane, Inter Milan captain Marcelo Brozovic, Barcelona's Franck Kessie, Celtic's Jota and Lazio midfielder Sergej Milinkovic-Savic.
There could have been a new world-record transfer too. PSG gave Al-Hilal permission to talk to Kylian Mbappe after making a £259m bid, but the forward opted to stay with the French champions and Neymar was sold instead.
Salah staying boosts Liverpool
Liverpool fans had been waiting nervously for the Saudi deadline to close.
There was the fear Al-Ittihad could come back with a bid the Reds could not refuse for Salah - when they would not have been able to buy a replacement for four months.
Salah has scored 188 goals in 309 games for Liverpool since joining from Roma in 2017.
"The key for Liverpool is Salah," said former Blackburn striker Chris Sutton on BBC Radio 5 Live.
"With him, I really believe they can make a challenge to Manchester City. If he went, they wouldn't challenge - he is that important to Liverpool."
Reds legend Jamie Carragher added on TalkSPORT: "It feels like a brilliant start [to the season] for Liverpool, everyone has got their energy and buzz back.
"It feels like the start of a new team, Klopp 2, Liverpool fans are calling it."
While Al-Ittihad may yet make a renewed offer in January or next summer, Salah's Liverpool contract runs for almost two more years, until the end of 2024-25. "Before you know it, his contract will be up and he will be able to go on a free," continued Carragher. "The feeling among most Liverpool fans is we have him for one more season."For all parties it feels like next summer Liverpool would still get a substantial fee and would still have him this season and a good chance of success. Liverpool would then have 12 months to consider how they replace him."It would be very difficult to get another Mo Salah right away, but great players come and great players go."
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