The Sunday Mirror claims Coutinho, 25, has his heart set on moving to the Nou Camp despite being made captain and scoring a hat-trick in Liverpool's 7-0 win over Spartak Moscow in the Champions League last week.
The Brazilian playmaker was the subject of three transfer bids from Barcelona during the last summer transfer window – the biggest of which amounted to £114m ($153m) – but Liverpool remained adamant that he would not be sold for any price.
Coutinho ended up filing a transfer request in an attempt to force through a move, but Liverpool manager Jurgen Klopp and owner Fenway Sports Group refused to alter their stance.
Klopp said last week that he was unaware of any fresh developments in Coutinho's status at the club.
"I have no reasons to think about it," the German was quoted as saying by Sky Sports. "We never spoke about transfers in this moment.
"There's really nothing to say. I am completely in the situation. Nobody has come to me to say Phil will be away in January.
"Whatever I could say would not stop your questions so I thought it makes sense not to answer it. I'm completely fine with the situation, how it is.
"We had this big story in the summer. I have no desire to have it again from now until January. I will say nothing about that. On January 31 we can shake hands and say: 'what a wonderful time we had together', the journalists and me, not Phil and me."
Coutinho signed a new five-year contract at Liverpool worth around £150,000 per week in January, making him the highest paid player at the club.
He has made 14 appearances in all competitions for the Reds this season, scoring nine goals.