The British tabloid, which did not cite any sources in its report on Monday, said Al Ittihad officials travelled to the United Kingdom in their latest attempt to sign the 31-year-old Egyptian international before the Saudi transfer window closes on Thursday.
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The Sun reported that Salah, the world’s highest profile Arab footballer, has been offered a Saudi Pro League record salary of £2.45m a week.
It also reported Salah had been also offered a significant percentage of shirt sales, a £55,000 win bonus, and ambassadorial roles with at least three major Saudi companies for the duration of his contract.
Liverpool FC did not immediately respond to Al Jazeera’s request for comment on the report.
After Liverpool’s 3-0 win over Aston Villa on Sunday, in which Salah scored, Reds boss Jurgen Klopp said the club would not sell Salah for any price.
Liverpool full-back Andy Robertson also insisted the squad had “no concerns” about Salah’s departure.
“For us Mohamed Salah is a Liverpool player and we believe that is what is going to be the case for the foreseeable future,” he said.
Salah, who has two years left on a contract signed last year, has scored 188 goals in 309 games for Liverpool since he joined the club in June 2017.
Al Ittihad could make another offer for Salah in the January transfer window if they are unsuccessful in tempting Liverpool to sell the forward this week.
Sports have been a major part of oil-rich Saudi Arabia’s efforts to rebrand as a global business and tourism destination under the Vision 2030 reform agenda pursued by Crown Prince Mohammed bin Salman, who is also PIF chairman.
Saudi Arabia has made major investments in recent years in golf, Formula One and football, with Saudi clubs spending hundreds of millions of dollars in recent months to sign top footballers such as Cristiano Ronaldo and Neymar.
In June it was announced that the PIF would take over four big domestic football clubs: the Riyadh-based Al Nassr and Al Hilal, and the Jeddah-based Al Ittihad and Al Ahli.
But the flurry of deals and investments has also spurred criticism that the Gulf kingdom’s spending amounts to an attempt to shift the focus from its dire human rights record.