Portuguese newspaper A Bola is reporting that the Reds are ready to return with an improved offer for the 22-year-old winger after having had a bid rejected by the club.
The same story claims that Liverpool are prepared to table bid of around £44m as Jurgen Klopp looks to lure the Portuguese winger to Anfield this summer.
And the report states that Liverpool are hopeful that their second offer will be enough to tempt Sporting into selling the young attacker.
The winger scored six goals and made nine assists in 32 league appearances for Sporting Lisbon last season.
Liverpool are believed to be on the lookout for a number of new signings this summer as Jurgen Klopp prepares for his second full season in charge at Anfield.
However, despite all of the speculation, the Reds have thus far only brought in young striker Dominic Solanke from Chelsea this summer.
Liverpool finished fourth in the Premier League as they secured a return to the Champions League.
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