Gunners chief Arsene Wenger is believed to have approached the Saints in the run-up to the transfer deadline to assess whether or not a deal for the French ace was possible.
However, the South Coast side quickly slapped a £15m price tag on their star, which eventually forced the London club to seal a deal for Kim Kallstrom.
But, Arsenal are believed to remain keen on the enforcer, and could return with a swoop at the end of the season.
While the likes of Luke Shaw and Adam Lallana have been stealing the headlines at St Mary’s Stadium this term, Scheiderlin has been one of Mauricio Pochettino’s top performers.
The 24-year-old has been a key cog in Southampton’s midfield, with his mature displays having seen his value rocket.
The Saints are keen to keep their man, but the lure of a Premier League challenge with Arsenal may be enough to turn the ex-Strasbourg man’s head once the next transfer window opens.