The 23-year-old Gabon international has only started in 15 matches in Seria A this season and is understood to be willing to move to England should the right offer come up.
Lemina is likely to cost the Gunners around £20 million, but would fit well within their wage structures. It is understood he is also subject to interest from Shalcke and Roma.
Lemina joined Juventus from Marseille for £8 million in 2015 and has since drawn comparisons to Paul Pogba for his style of playing and similar body frame.
Should the transfer materialise this would present a problem for on-loan Jack Wilshere who is set to return to the Emirates in the summer despite still undergoing treatment for a long-term injury.
Arsenal are also facing the threat of losing two of their stars, Mesut Ozil and Alexis Sanchez, in the summer, which would leave the club in need of reinforcements in midfield.
Lemina is a box-to-box player who possesses plenty of stamina, likes to dribble and is a very good passer but is also equally adept at playing as a right winger due to his good crossing ability.
His contract with Juventus runs out in 2020.