The Anfield club had a bid of around £8m rejected for the 20-year-old Brazilian last week but negotiations have continued and Liverpool are confident an improved offer will be acceptable.
Coutinho signed for Inter from Vasco da Gama as a 16-year-old, though he remained with the Brazilian club until he was 18, and is regarded as one of the most promising young players in Serie A. Despite that reputation, Inter are considering the approach from Anfield as they look to improve their finances.
The player has placed responsibility for any transfer firmly on the Italian club by stating that he wishes to impress the coach, Andrea Stramaccioni. Coutinho told Sky Italia: "The Liverpool offer? I'm happy with these offers, because it means I am doing my job well. But I think Inter have faith in me and I want to show my value here. I don't feel that I'm on my way out. I hope to stay at Inter. The young players feel the faith of the coach and of the club."
The Liverpool defender Danny Wilson, meanwhile, has admitted he has little future at the club under Brendan Rodgers. The Scotland international has made only nine first-team appearances for Liverpool since joining the club for an initial £2m from Rangers in 2010 and is on loan at Hearts until the summer.
The 21-year-old, who has not made a senior appearance for Rodgers, said: "It's going to be difficult for me to have a future at Liverpool. They have four centre-backs there who are fighting for two positions really. You see players who played in past seasons not playing as much now. I have not really managed to force my way in. My only thinking now is to get out and play and what happens, happens."
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