Mohamed Salah has scored one goal in two Premier League games so far this season
Al-Ittihad are reported to be interested in the Egypt forward, 31, who joined the Reds from Roma in 2017.
However, Liverpool do not want to sell a player who only signed a new three-year deal last summer and with the transfer window closing on 1 September.
Salah's agent has previously played down talk of a move to Saudi Arabia.
"Mohamed remains committed to Liverpool," said Salah's agent Ramy Abbas Issa 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's representative has not responded following new links of a move to Al-Ittihad, who have already signed current Ballon d'Or winner Karim Benzema and ex-Liverpool midfielder Fabinho, plus former Chelsea midfielder N'Golo Kante and ex-Celtic winger Jota.
Former Tottenham and Wolves boss Nuno Espirito Santo is the club's manager.
Salah has started both Liverpool's games this season, although he showed frustration at being substituted in the draw at Chelsea before knocking in the rebound from his saved penalty in the win against Bournemouth.
Liverpool have already been left with issues in midfield when, after James Milner, Alex Oxlade-Chamberlain and Naby Keita left, Fabinho and Jordan Henderson moved to Al-Ittihad and Al-Ettifaq respectively.
The club have since signed defensive midfielder Wataru Endo from Stuttgart.
Salah has scored 187 goals in 307 games for Liverpool and 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 three Premier League Golden Boots and been named the PFA player of the year twice.
-- Courtesy of BBC Sport