Coutinho handed in a transfer request in the summer in a bit to force a move to Barca, but Liverpool rejected every approach made for the Brazilian.
Coutinho captained the Liverpool side that demolished Spartak Moscow 7-0 in the Champions League on Wednesday, in which he also scored a hat-trick.
The Spanish giants have not given up their hopes of signing Coutinho and are reportedly prepared to try their luck again in January when the transfer window reopens.
Barcelona are thought to have been in talks with Liverpool officials, with the Reds valuing Coutinho at around £127m.
Coutinho is reportedly still keen on the move and Chelsea star Fabregas has backed the midfielder to finally make it happen.
“I think he’s a great player,” Fabregas said, speaking to TV3. “I see the Barcelona style, the truth is that he is at that level.
“Where I see it is more com
“Being flexible is also important.”
Fabregas left Arsenal for his boyhood Barca in 2011, but after first team opportunities slumped, he returned to England with Chelsea in 2014, winning two Premier League titles since.