In the video, which was spread on Twitter, Salah appears to be using his phone while in his white Mercedes-Benz and surrounded by fans, whom he pointedly ignores.
Liverpool also confirmed that the matter would be dealt with internally and that neither club nor player would be commenting on the matter.
In the footage the Egyptian - wearing a red top - appears to use his mobile phone as he gazes down at the screen.
Liverpool superstar Mohamed Salah could be in trouble with the police after he was referred to the authorities by his own club for an incident while driving.
The clip continues to follow Mr Salah as he drives a few metres forward, the camera zooming in on his vehicle window to show the footballer still using his phone at the wheel. Such behaviour was on display during Liverpool's match against West Ham, when a kid invaded the pitch and gave him a hug before being escorted away.
And according to law in the UK, It is illegal to touch a phone while the engine is running as it can lead to three points on your licence, a driving ban or a £1,000 fine.
However, Liverpool, via a spokesperson, said that they have made the police aware of the situation; one believed to have prompted their tweet.
However, the whole matter has sparked a heated debate between fans of Liverpool and other football clubs.