The Reds parted with the Brazil international playmaker back in the winter transfer window of 2018.
A professional dream was chased as Coutinho headed to Camp Nou, but a spell in Catalunya has becoming something of a nightmare.
The South American schemer has struggled to find his spark at Barca, leading to him being loaned out to Bayern Munich.
The 28-year-old is facing up to an uncertain future, with there seemingly no role for him back in Spain.
That has led to talk of a return to the Premier League being made, with various landing spots offered up – from Tottenham to Newcastle.
Liverpool have offered no indication that they are looking to bring Coutinho back into what is now a Premier League title-winning squad.
Enrique, though, believes that a player who has thrived at Anfield before could be the perfect option for Jurgen Klopp as he seeks to bring added creativity into his ranks.
The former Reds defender told Stadium Astro: “We need a playmaker, a number 10, who is going to be better than Coutinho for us?
“He knows the club, he knows the city, he’s going to perform straight away because he’s been a Premier League player.
“The only problem is wages-wise, I believe he’s very, very high wages-wise in Barcelona, so I’m not sure if he will go to Liverpool obviously losing money.
“The problem with Barcelona, they try to play him on the left side all the time, in Neymar’s position and he’s not this type of player, he needs to play in the middle.”
During his previous stint on Merseyside, which lasted five years, Coutinho took in 201 appearances for Liverpool.
He recorded 54 goals and 45 assists across those outings and Liverpool have, despite enjoying considerable success over the course of the last 13 months, opted against bringing in a like-for-like replacement as yet.