That's according to beIN Sports journalist Mohammed Al-Wadahi.
Claims of a medical didn't take place and the Reds informed the media that the report was fabricated.
However, Al-Wadahi says the deal was actually close and Mahrez had already started looking for places to live in Liverpool.
“The news of the transfer to Liverpool is a very reliable source of much more than the player's agent," the beIN Sports journalist tweeted.
“He did not publish it until I received the green light from the same player who started looking for a house in Liverpool and was ready to move to Liverpool for a medical examination after he was told."