The defending champions Manchester City are placed at the top of the English Premier League table with 28 points while the 19-time winners Liverpool are in the second position with 27 points in 12 games so far.
Bafétimbi Gomis previously held the record from 2011. He had taken eight minutes to complete his hat-trick.
“I feel great and excited to win trophies with the club. It's a happy day for everyone,” Salah told the club's website.
Salah, who has 18 months left on his current Liverpool contract, has been in talks with the club about an extension but hasn't yet received what he deems an acceptable offer.
The Egyptian scored a hattrick against United and brought his side a 5-0 victory. Apart from that, he even scored singles against Manchester City and Watford.
Salah converted a cross by Trent Alexander-Arnold in the 20th minute at Elland Road to become the 30th player to reach the milestone, with only four getting there quicker than the Egypt winger's 162 appearances.
The 29-year-old Salah missed the Pharaohs’ 1-0 win over Angola on Sept. 1 in Cairo after Liverpool refused to release him because of coronavirus restrictions.
Egypt is on Britain’s red list, so Salah would be required to quarantine upon his return from Cairo and miss two Premier League games.
The Premier League's top scorer was unusually benched — by coincidence or not — hours after an interview was published in which he flirted with a move to Spain and grumbled about not captaining the English champions.
The Egypt forward twice tested positive for COVID-19 during the international break and missed the 3-0 win over Leicester in the Premier League on Sunday.
Salah was last week diagnosed with Covid-19 while on international duty with Egypt.
The announcement was made by the Egyptian soccer association on Twitter ahead of Saturday’s game against Togo.
Liverpool last won the English top-flight title in 1990 and have never won the Premier League trophy as it came into existence in 1992.
Naby Keita, a former Salzburg player, headed in the opening goal in the 57th minute before Mohamed Salah rounded the goalkeeper and squeezed home a finish with his weaker right foot from an acute angle near the byline.
Mohamed Salah has an ankle injury and was ruled out of the Egyptian squad for games against Kenya on Thursday and Comoros on Monday.
Liverpool threw away a 3 goal lead to Salzburg but Mohamed Salah’s 69th-minute goal made sure they won their second Champions League game 4-3.
Liverpool are now the only side to score a maximum nine out of nine points in the first three games of the Premier League this season as they beat Arsenal 3-1 at Anfield.
Mohamed Salah and Divock Origi scored for Liverpool as they beat Tottenham 2-0 at the Wanda Metropolitano to lift their first European title in 14 years.
The return of Harry Kane and Mohamed means Lucas Moura and Divock Origi could miss out on a starting berth for Tottenham and Liverpool respectively in the Champions League final.
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