Coutinho has left Premier League club Liverpool for Spanish and European giants Barcelona in the January transfer window for a fee reported by BBC Sport to be worth £142 million.
The 25-year-old Brazil international, who can operate as an attacking midfielder or as a winger, is one of the best players in the world and will be missed at the Reds.
According to beIN SPORTS, Liverpool are interested in signing Mahrez from Premier League rivals Leicester in January as a replacement for Coutinho.
Mahrez is one of the best players in the Premier League and operates predominately as a winger.
The 26-year-old Algeria international has scored seven goals and provided as many assists in 21 Premier League starts for Leicester so far this season.
During the 2016-17 campaign, the Algeria international scored six goals and provided three assists in 33 league starts for the Foxes.
Former Liverpool striker Owen does not believe that Mahrez would be an ideal replacement for Coutinho at Anfield.
Owen wrote on Betvictor.com: “I was asked this week if I thought Riyad Mahrez, who has been linked with a move to Anfield, would be the ideal replacement for Coutinho but I couldn’t agree.
“As good a player as Mahrez is, he might not possess the pace or work ethic that Jurgen Klopp might be looking for and I wonder where he would fit into the starting XI – certainly not instead of the brilliant Mo Salah on the right side of the front three.”