The Reds had been linked with the Portugal star earlier in the transfer window.
France's Paul Pogba in action with Portugal's Joao Mario
The Reds have been busy so far this summer, bringing no fewer than seven new signings to Anfield.
It has been anticipated that more players could arrive, with Jurgen Klopp hinting that they may make further moves before the end of the transfer window.
Portugal's Joao Mario in action with Poland's Jakub Blaszczykowski
A potential target could be Sporting Lisbon midfielder Joao Mario, with Diario de Noticias reporting earlier this summer they had seen a £33 million bid rejected.
That doesn’t appear to have deterred them though, and A Bola are now claiming that the Merseyside club are ready to come in with an improved offer for the Portugal star.
Sporting Lisbon's Joao Mario celebrates goal against Bayer Leverkusen.
They are not the only ones interested in his services though, with the Portuguese newspaper also suggesting that Inter Milan, Real Madrid and Paris Saint-Germain are all interested in his services as well.
A move for Mario would be something of a surprise given the number of midfielders Klopp currently has at his disposal.
There are also other areas of the team more desperate for improvement, with the left-back position in particular still needing attention.
Liverpool manager Juergen Klopp