The youngster is highly rated and could provide competition for Alberto Moreno.
Liverpool manager Juergen Klopp after the match
The Reds have been busy so far this summer, signing no fewer than seven new players ahead of the new season.
One area they have failed to improve is the left back position though, despite Alberto Moreno coming in for stern criticism once again last season.
Liverpool's Brad Smith and West Brom's Jonathan Leko in action
They have also allowed Brad Smith to join Bournemouth this week, meaning they need to add competition in the position.
They were trying to secure a deal for Leicester City man Ben Chilwell but he elected to sign a new deal with the Premier League champions.
Leicester City's Ben Chilwell in action against Manchester City's Isaac Buckley Ricketts (L)T
Their search appears to be an on-going one and according L’Equipe they are now targeting 19-year-old Gaspar.
He can play on either flank and has impressed for Lyon’s youth squad, which is likely what has caught the attention of the Reds.
It now remains to be seen if they make a firm offer for his services, but it appears they will face competition if they do so as Villarreal and Bayer Leverkusen both thought to be interested in taking him on loan.
Liverpool manager Juergen Klopp