The Brazilian was strongly linked with a move to Barcelona during the summer, and it is understood that he handed in a transfer request at Anfield in a bid to force a move to Spain.
Liverpool resisted the interest, however, and Coutinho has been in brilliant form for the Reds this season - scoring nine times and registering seven assists in 14 games in all competitions.
Coutinho wore the captain's armband as he scored a hat-trick against Spartak Moscow in the Champions League on Wednesday night, but the attacker refused to fully commit himself to the Merseyside giants after the match.
"I am at Liverpool and I always do my best when I have the opportunity to play, respecting the jersey and the supporters," Coutinho told reporters. "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.
"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.
"Of course a lot happened in the summer but my will is always to play and do the best wherever I am - that has not changed. I am here [at Liverpool], we have a lot of games and I try to do my best to help."
Barcelona are being widely tipped to return with a big-money offer in the January transfer window.