Citing Mundo Deportivo's Xavier Munoz, Jack Staplehurst of the Daily Star said "Coutinho made Liverpool agree to a fixed price for January" after the Reds shut down Barcelona's attempts to sign him in the summer, and he is still hoping to move on having also agreed terms on a five-year deal with the Catalan club.
Barca are eager to meet Liverpool at a lower price than £128 million but want to snap up the Brazilian before the likes of Real Madrid or Paris Saint-Germain come knocking.
Per MailOnline's Dominic King, Coutinho was asked about his future after Liverpool dismantled Spartak Moscow 7-0 in the Champions League on Wednesday:
"I do not know how the future is going to be. What will happen in January, we will know it in January. I do not know if there will be an offer. I am at Liverpool and I always do my best when I have the opportunity to play, respecting the jersey and the supporters.
"Last summer there was a job offer in the same way that happens with any employee and I was interested in it. Since I stayed, I have played with will and desire."
Coutinho has had a superb campaign thus far, contributing nine goals and seven assists in all competitions.
He bagged a hat-trick against Spartak, earning the praise of Reds writer Leanne Prescott:
The 25-year-old's chemistry with his team-mates Roberto Firmino, Mohamed Salah and Sadio Mane is something to behold, with the quartet moving and rotating fluidly in the final third and each bringing an important quality to Liverpool's attack.
Football writer Andrew Beasley demonstrated how effective the four players are together:
In Coutinho's case, he is typically the one to pull the strings, is the most creative of the four and he is also a particular threat from long shots and set pieces.
What's more, he has begun to showcase his talents on a more consistent basis than he used to at Anfield, where he was occasionally guilty of putting in some anonymous performances.
It is perhaps more pressing for Barcelona that they find a replacement for Xavi Hernandez to offer them stability and control in midfield, but with Neymar gone and Andres Iniesta now 33, there's scope for a player of Coutinho's talents to cement a place in the side and link their midfield and attack with vision and panache.
His comments will do little to assuage the fears of the Anfield faithful, but given his importance to the Reds' fortunes—even if they do have three other tremendous attacking talents—it would seem unlikely Liverpool would be willing to part with him midway through the season, even if Barcelona are prepared to make a substantial offer.