The Brazil international was linked with a move to the La Liga giants in the summer transfer window but the Reds refused to consider any offers for the 25-year-old attacker.
Coutinho handed in a transfer request but the Merseyside outfit refused to alter their stance and the Liverpool FC number 10 ultimately remained at Anfield.
The South American playmaker has scored 10 goals and has made seven assists in 15 starts and two substitute appearances in all competitions this season.
Unsurprisingly, Barcelona are reportedly prepared to launch a fresh bid to sign the 25-year-old playmaker ahead of the January transfer window.
Liverpool FC have been linked with a move to sign Croatia international Rakitic in recent seasons but a deal has failed to come to fruition.
The Barcelona midfielder is hoping to see Coutinho at Camp Nou despite the increased competition for places that his potential transfer would create.
“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,” Rakitic told Sky Sports.
“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 scored 13 goals and made seven assists in 31 appearances in the Premier League last term to help Liverpool FC secure a return to the Champions League.
The Reds signed four players in the summer transfer window ahead of their return to the Champions League.
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