The Catalan giants have been on the trail of the Reds midfielder since the second-half of last season and view him as an ideal replacement for Andres Iniesta, who has entered the final-year of his contract with the club.
Coutinho was linked with a move to the Camp Nou earlier in the year, but committed his future to the Merseyside club by signing a five-year deal, which made him their highest paid player at £150,000-a-week ($194,640). Barcelona are desperate to sign a midfielder this summer and have been linked with a number of players including Paris Saint-Germain's Marco Verratti and most recently Inter Milan's Geoffrey Kondogbia.
According to The Times, Barcelona's fresh offer was worth €80m (£72m) for Coutinho, but it was swiftly rejected by Liverpool with Jurgen Klopp making it clear that the Reds will not lose any player they want to keep this summer. The Brazil international is viewed as an integral part of the manager's plans to take Liverpool back to being regular contenders in the Premier League and Champions League.
The German coach has already made two additions in the form of Dominic Solanke and Mohamed Salah thus far this summer and has indicated that he is in the market for further additions. However, his main priority is to retain the core of the squad and to make additions to compliment the players that are already there.
"The main thing I think about is how we can make the next step with the players we had last season," Klopp said, as quoted by the Liverpool Echo.
"The good news is that actually we didn't lose - and we will not lose - a player we want to keep this summer. That's the best news actually and then we'll see who can bring into the squad," the former Borussia Dortmund coach added.