The Reds are adamant the 25-year-old is going nowhere despite Coutinho himself wanting to leave.
Barca players are desperate for Coutinho to join them with Luis Suarez starting the charm offensive to try and push through a transfer.
Paulinho followed that on Wednesday by praising his countryman and now Rakitic has joined in.
The Spanish midfielder said Coutinho would be a “perfect” signing and said he would be “really happy” if a move is done.
It’s likely to irk Liverpool top brass who will be becoming increasingly frustrated with the open nature of Barcelona’s business.
Rakitic said: “Every good player is welcome. So we have to say that the doors are open for every good player, and Coutinho is a good player.
“With all respect to his club Liverpool, and his fans, we would be really happy if he came.
“But with all the respect if he stayed at Liverpool we would wish him all the luck in the world.
“We have to think about the players that are already here, I think we have a really good team.
“We have to do it together. If there is an opportunity to do it with Coutinho, or another player, perfect.”
Coutinho’s old team-mate Suarez gave him a Barca-branded Christmas gift this week.
In a Secret Santa supposedly organised by Neymar, Suarez is filmed ‘randomly’ pulling Coutinho’s name out of a hat.
“It’s my little brother, Philippe Coutinho,” he says.
“Well Philippe, from Barcelona I send you a gift that I know you’ll like a lot, because you like it a lot and I know you’re going to remember the good times that we have and that we live.”
Suarez then holds up a Barcelona gift bag.
On receiving the gift, Coutinho says “what the f***?” while smiling.