The Brazilian rose to prominence when he joined the Reds in 2013.
Coutinho spent six seasons at Anfield, scoring 54 goals in more than 200 appearances.
But the 26-year-old made a massive £142m move to dream club Barcelona last January.
The midfielder, though, has struggled since his move to the Nou Camp.
And this has sparked rumours of a move away from the Spanish giants.
Coutinho has been linked with a move to Liverpool’s rivals United.
But popular fan show The Anfield Wrap believes they should open the gate for a reunion.
Liverpool fans’ comments come as:
Supporter Lizzie Doyle said: “We can talk about attitude and obviously we want players that want to play for Liverpool.
“But there’s not much loyalty in football anymore.
“He’s an unbelievable player but it depends what Klopp wants from his side.
“You’re bringing Coutinho back to fill a Coutinho-shaped hole but if he hits a bit of form, could he head elsewhere?”
But fellow fan Paul Senior suggested this would not be a problem, citing a former United player and his lack of desire to make an Old Trafford return.
“I think you only get one hit at that,” he said.
“Look at Wilfried Zaha at Palace. I don’t see him saying ‘I’m good, so I’ll go back to United’.
“Liverpool have gone further than we were with Coutinho, getting to a Champions League final and challenging for the league.”
The fan then made a huge suggestion for the Reds’ transfer strategy.
Paul continued: “I don’t think we’ll go for him, personally.
“But there’s not that many players that become available in his bracket that often.
“If he came back, we could probably have him for the rest of his career”
“If he went to any other Premier League club, he would ultimately strengthen any of them.
“I would rather Liverpool be in the mix than see him go anywhere else.”
And the Anfield faithful made it clear they wanted to see the Brazilian in red again.
“Coutinho’s still only 26 years old,” one supporter said.
“If he came back, we could probably have him for the rest of his career.”
Another commented: “You would be stupid not to want Coutinho back.”
While a third wanted to see one difference in the Brazilian’s play.
“I think I’d take Coutinho back,” they said.
“So long as he promises to pass to Roberto Firming this time.”
And a fourth added: “I would take Coutinho back rather than see him at United.”
Barcelona have reportedly named their price for United, though.