Mainz are battling to keep Jean-Philippe Mateta away from Premier League clubs.
L'Equipe says Southampton have become the fifth Premier League club to have a bid for Mateta rejected by Mainz.
Forward Mateta is worth €40m to the German side, but have only received offers between €20m and €25m so far.
Everton, Newcastle, Cardiff and Watford have also seen their interest rebuffed.