Walcott left the Saints 10 years ago after coming through the club’s academy and has since gone on to play for England on 47 occasions but now the Gunners are planning to listen to offers.
The 28-year-old has only made 10 appearances this season, with the majority of them coming in cup competitions. Southampton boss Mauricio Pellegrino is looking for more competition for Charlie Austin, Shane Long and Manolo Gabbiadini and Walcott could fit the bill.
The Saints face competition from West Ham, but Walcott could be sold as early as the January transfer window.
Watford boss Javi Gracia does not think Abdoulaye Doucoure's form will be affected by his omission from France's latest squad.