The 19-year-old starlet emerged as a promising first-team player at the Emirates Stadium last season, making a handful of appearances for the north Londoners.
Arsene Wenger is thought to be a massive fan of the teenager, but with the Gunners possessing a wealth of talent in his favoured positions, Gnabry’s chances of regular time on the field of play this term look slim.
This has alerted Southampton, who are said to be considering a move for his signature.
A loan deal appears the likely option given the youngster’s potential, with the Saints desperate to add to their ranks following the sales of a host of big stars.
Arsenal may be willing to discuss a deal for Gnabry after snapping up Callum Chambers from the South Coast club, who are known for their nurturing of young talent.
Southampton are also looking at Norwich’s Nathan Redmond.
The fleet-footed winger is currently in the Championship with the Canaries, and could be open to a quick return to the top tier.
Leeds’ Sam Byram remains a target despite an opening bid of around £5m having been rejected for the full-back.