The Ghana international has been linked with a move away from the Emirates after three years spent in north London.
Despite being a key player for Mikel Arteta, it has been said that the 30-year-old could be allowed to surprisingly depart.
According to Italian reporter Fabrizio Romano, there are currently no talks planned to extend the ex-Atletico Madrid star's stay beyond 2025.
This has seen clubs to stake an interest in the player, with discussions already taking place about his possible exit.
Romano then declared that Arsenal have a 'concrete and strong' interest in Saints teenager Lavia.
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He claimed that there have been negotiations between the 19-year-old's camp and Arsenal, with their relationship described as 'excellent'.
Premier League champions Manchester City have a £40million buy-back clause in Lavia's contract which becomes active in 2024 after selling him to the south coast outfit last summer.
Their rivals Manchester United also have Lavia on their radar, with talkSPORT understanding that Chelsea are another interested club.
Citizens boss Pep Guardiola hailed the youngster in April as he spoke he only agreed to offload him as he couldn't guarantee him minutes.
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And Lavia certainly benefited from regular first-team football, as he boasted more minutes than any other player in the English top-flight aged 20 or younger.
He featured in 29 Premier League games with his only goal of the season coming in the 2-1 win against Chelsea in August.
But despite his impressive performances, he couldn't help Southampton stay in the Premier League, as they finished 20th in the table.
Lavia may not be the only midfielder to join Arsenal this summer, with the club desperate to sign No1 priority Declan Rice.
A first offer has already been rejected by West Ham, but Arsenal are expected to return with a second bid which could exceed £100m.