The Liverpool ace was filmed in his car by fans as he drove home from the 4-0 win over West Ham on the opening day of the Premier League season.
And the clips, which emerged on Facebook yesterday, appeared to show him scrolling on his phone.
“The club, after discussion with the player, have made Merseyside Police aware of the footage and the circumstances surrounding it’s capture,” a Liverpool spokesman said.
“We have spoken to the player also and will deal with any follow-up internally.
“Neither the club or player will be making any further comment on this matter.”
Under UK driving laws, it is illegal to use a handheld mobile phone when driving – even while stopped at traffic lights or queuing in traffic.
Penalties for the offence can incur six points on the driving license and fines of up to £200.
And Merseyside Police confirmed they were aware of the footage.
“We have been made aware of a video believed to show a footballer using a mobile phone whilst driving,” the Merseyside Police Contact Centre said on their official Twitter account.
“This has been passed to the relevant department.”
Road safety charity Brake told The Sun: “It is disappointing to see someone who is a role model to many thousands of football fans breaking the law and setting a bad example.
“Mobile phone use behind the wheel, in any form, is illegal and dangerous. Anything that distracts a drivers attention from the road, even for a split second, can lead to devastation, no matter how slowly they are travelling.
“Mobile phone use behind the wheel is all too prevalent and a crackdown is required to rid our roads of this menace.”
Salah scored against West Ham in the 4-0, carrying on where he left off last term.
The Egypt star hit a stunning 44 goals last term as Liverpool finished third and got to the Champions League final.
Salah was back at training on Monday at Selwood for a recovery session and will be gearing up for Monday’s clash with Crystal Palace today.