They claim the south coast outfit have already tabled a bid with Ligue 2 side Troyes for the forward.
Last season, in the French second division, the 19-year-old scored 10 goals and provided three assists in his 35 matches.
The player appears to be in demand as the newspaper states that Montpellier and Strasbourg have already seen their bids rejected and believed their offers were ‘too little to compete with the proposals of English clubs (Southampton) or German.’
The Saints do face competition for the attacker as Borussia Monchengladbach have had an €8million (£7.19million) offer accepted.
Mbeumo appears to fit the profile of player Ralph Hasenhuttl is looking for to revamp his squad. He is young, scores goals and can play in multiple positions.
Having already signed 21-year-old Moussa Djenepo and 23-year-old Che Adams, who can both operate all across the frontline, it suggests the Austrian is eager to lower the age of the team whilst adding versatile players that can score goals.