Jurgen Klopp is keen to bolster his defensive options this summer and the Reds have tabled a bid for the 21-year-old Argentina international this week.
The Sport Review understands that Liverpool are ready to offer central defender Mammana a five-year contract worth €3.2m (£2.8m) a year, meaning he would earn around £54,000 a week with the Merseyside club.
However, the player is holding out for permission from Lyon to discuss personal terms with Liverpool because he wants the two clubs to reach an agreement before proceeding with any negotiations.
Mammana was linked with the likes of Arsenal and Tottenham before his eventual switch to Lyon from River Plate in July 2016.
Born in Merlo, Argentina, Mammana made 17 appearances in Ligue 1 for Lyon last season in his debut campaign in France, scoring one goal.
The centre-half, who has been capped by his country’s senior team three times and made his full international debut back in June 2014, signed for Lyon last year after having begun his career at Argentinean side River Plate.
The player himself is currently on holiday in his native Argentina as he recharges his batteries ahead of the new season.
Liverpool are thought to be on the lookout for a number of new signings this summer as Klopp prepares his team for a return to the Champions League next season.
However, the Reds have so far only concluded deals to sign Mohamed Salah and Dominic Solanke, both in attacking positions.
Defence is an area Klopp will be keen to strengthen this summer, with the Reds having conceded more goals than any other team in the Premier League’s top four last season.
Liverpool’s players are due back at Melwood to begin their pre-season preparations on Wednesday after having enjoyed some time off following a gruelling Premier League campaign.
Klopp is likely to want his side to have completed the majority of their transfer business before the first fixture against Crystal Palace in the Premier League Asia Trophy in Hong Kong on 19 July.
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