Liverpool had shunned two offers for the playmaker but according to The Sun, Barcelona have returned with an improved bid.
The Reds and manager Jurgen Klopp have remained firm in their stance that Coutinho will not be sold during the current transfer window, regardless of the size of the bid made by Barcelona who have £200m to spend after the exit of Neymar to Paris Saint-Germain.
However, it has been claimed that the latest approach has been given short shrift by the Premier League side, who remain intent on keeping their star man at Anfield.
The Brazilian is currently sidelined with a back injury and will not feature for Liverpool against Crystal Palace this weekend, while there have been differing reports over whether Coutinho had handed in an official transfer request.
Liverpool paid Inter Milan just £8.5m for Coutinho in January 2013, and the 25-year-old has gone on to contribute to 43 goals in 181 appearances in all competitions.