Coutinho left Anfield after the Brazilian completed his move to Barcelona on Saturday (6 January) for a reported fee of £142m ($192m).
The Reds were previously reported to be preparing for his departure with a £50m ($68m) move for Mahrez after identifying him as a potential replacement.
However, recent reports from Sky Sports claimed that Liverpool were never interested in Mahrez and have not even made contact with the Foxes over a potential move. Instead, Jurgen Klopp has reportedly identified Thomas Lemar as his top priority target.
But former Liverpool striker Aldridge would like to see his old club pursue Mahrez nonetheless as he is "very similar" to Coutinho and boasts Premier League experience.
"If you look at the way Coutinho plays, he [Mahrez] is very similar," Aldridge told BBC Radio 5 Live.
"He is older, he has played in the Premier League for some years and everybody has seen the ability he has got, so he ticks a lot of boxes.
"You need that type of player similar to Coutinho who sees that pass, can do something extraordinary outside the box, can bend it in the top corner and is good on free-kicks as well."
Aldridge also advised Liverpool to spend the Coutinho money wisely as they and Tottenham failed to do so when they previously sold Luis Suarez and Gareth Bale respectively for a large fee.
"I am not surprised but disappointed he is leaving because he is a fantastic player to watch," Aldridge added. "£140m is a lot of money and Liverpool have to spend it wisely.
"They have spent £75m of it wisely on Virgil van Dijk - a player we have needed for some time in a leader at the back - but he [Coutinho] needs replacing and we have got to do it ASAP."