The Sun claim the Italian giants want at least £20m for the 22-year-old to do business with Arsene Wenger.
The Gabon international has only just moved to Juve permanently but that hasn't stopped Lamina being linked with a move to the Emirates.
West Brom and German outfit Schalke are also said to be interested in the midfielder who can play at right-back as well.
Arsenal may now cool their interest as their priorities surround finding a new central defender and striker before the transfer window shuts.
With Per Mertesacker and Gabriel out injured, Wenger has been linked with Valencia centre-back Shkodran Mustafi.
And the Gunners are also keen to add a striker to their ranks to ease the pressure on Olivier Giroud with Alexandre Lacazette eyed by the Premier League side.
Lamina played 10 times in Serie A last season while on loan at Juve, scoring twice for the eventual champions.
Arsenal continue their Premier League campaign this weekend against Leicester as they look to bounce back from the 4-3 defeat to Liverpool.