The Bundesliga side are exploring whether a deal for the 27-year-old is financially viable as they search for defensive reinforcements, with Medina seen as a potential replacement for Alejandro Grimaldo following the left-back's move to Atlético Madrid.
Marseille, who are open to discussing a sale, want to recoup close to the €22m they have invested in Medina in total: an initial €2m loan fee paid to Lens last season followed by a €20m mandatory purchase obligation that was triggered on 1 July. No agreement over a fee has yet been reached, and Leverkusen are said to be weighing up whether the transfer represents value for money before deciding whether to pursue it further.
Medina, who can play at centre-back or left-back, made 26 appearances for Marseille last season after his move from fellow Ligue 1 side Lens, contributing a single assist, and has also featured 164 times in Ligue 1 across his career along with 10 Champions League appearances.
He was capped for the 14th time by Argentina during this summer's World Cup, starting three matches and coming off the bench in the final as Lionel Scaloni's side lost to Spain after extra time, having primarily been used at left-back for the national team despite operating mostly in the centre for his clubs.
Bayer Leverkusen's interest in the Villa Fiorito-born defender is not new, with the German club having monitored him previously during his time at Lens. Medina is understood to be one of several options under consideration as Leverkusen look to strengthen at the back, alongside Genk's Zakaria El Ouahdi, who is also being considered as a candidate for the right-back position.
Argentina team-mate Exequiel Palacios remains part of the Leverkusen squad, though he has himself been linked with a move to RB Leipzig in recent days. Both Marseille and Leverkusen missed out on Champions League qualification last season, adding an extra layer of financial calculation to any deal struck between the two clubs before the window closes.