The club took the action when a video emerged that appears to show the Egyptian star using his phone while driving his car, with children surrounding the car to get a glimpse of him.
"The club, after discussion with the player, have made Merseyside Police aware of the footage and the circumstances surrounding its capture." a spokesperson for Liverpool said.
"We have spoken to the player also and will deal with any follow-up internally."
Merseyside Police also confirmed that they have been made aware of the incident, but made no further comment on the action that will be taken.
UK law dictates that anyone caught using a mobile phone while driving face a fine and will receive 6 penalty points on their licence.
On the pitch, Salah made an excellent start to his season by scoring in a 4-0 win over West Ham on Sunday.