The Danish forward is now without a club following the Gunners’ decision to cut him loose after a lengthy spell in north London.
Speculation at some stages of last season suggested that Arsene Wenger was ready to present the 26-year-old with a fresh contract, yet disciplinary issues saw him drop away from the first-team.
Bendtner has endured a largely unsuccessful spell in England with loan moves to Sunderland and Birmingham having ended in disappointment, but Southampton are thought to be looking at the possibility of handing him another chance.
The Saints recently lost Rickie Lambert to Liverpool and are known to be looking to get in a replacement in a bid to maintain the form they showed last term.
The Scandinavian is seen as a good option, with his impressive international record – 26 goals in 56 outings – suggesting that there is potential to be unlocked.
New boss Ronald Koeman is expected to be backed significantly in the transfer market with Adam Lallana and Luke Shaw’s sales to Liverpool and Manchester United respectively set to bring in around £60m.