Salah has one goal and two assists for Liverpool in three games this season
The bid for the 31-year-old forward was for in excess of £100m, with add-ons taking it up to £150m.
Liverpool remain insistent the Egypt international is not for sale, and that is final as far as the club are concerned.
Salah, who joined the Reds from Italian side Roma in 2017, signed a new three-year contract last summer.
Liverpool manager Jurgen Klopp said last week that Salah was "100% committed" to the Anfield cause, and on Friday he reiterated the club's stance that the player was not for sale.
"The position remains the same. Absolutely no doubt about that. That's how it is. Nothing else to say," said Klopp.
Liverpool would have little time to react to Salah's potential departure, with the transfer window closing at 23:00 BST on Friday for incoming deals involving Premier League teams.
However, Al-Ittihad will still be able to sign players as the Saudi Pro League transfer window is set to close on 7 September.
Salah's agent has previously dismissed talk of a move to Saudi Arabia but has not responded following the latest links with Al-Ittihad.
"Mohamed remains committed to Liverpool," agent Ramy Abbas Issa wrote in a social media post on 7 August.
"If we considered leaving Liverpool this year, we wouldn't have renewed the contract last summer."
Salah has started all three of Liverpool's games this season, with Klopp's side having accumulated seven points following a draw with Chelsea and wins against Bournemouth and Newcastle United.
He set up Luis Diaz to score at Chelsea but showed frustration at being substituted in the draw before knocking in the rebound from his saved penalty in the win against Bournemouth.
Salah had the assist for Darwin Nunez's winner at Newcastle, with Liverpool getting the three points despite being down to 10 men for most of the match.
A key player for the Merseysiders, Salah has 187 goals in 308 games for Liverpool and registered 76 assists.
He has won the Champions League, Premier League, FA Cup, League Cup, Fifa Club World Cup and Uefa Super Cup during his time at Anfield.
He has also won or shared the Premier League Golden Boot three times and been named the PFA player of the year twice.
Liverpool have already had to deal with midfielders Fabinho and Jordan Henderson moving to Al-Ittihad and Al-Ettifaq respectively in the Saudi Pro League.
Roberto Firmino left Liverpool on a free transfer when his contract expired and joined Al-Ahli.
The approach for Salah comes in a summer when clubs from the Middle East country have signed a number of superstars, including Karim Benzema and Neymar, while Al-Hilal made a world record £259m bid for Kylian Mbappe.
-- Courtesy of BBC Sport