The Spaniards are keen to lure the Italian international back to La Liga – where he represented Espanyol – and have been buoyed by rumours that he has failed to settle on the South Coast following his summer move from Roma.
The 27-year-old was one of the Saints’ marquee signings during the last window, but has so far failed to make himself a guaranteed starter at St Mary’s Stadium.
He is currently in direct competition with fans’ favourite Rickie Lambert, and is rumoured to be struggling to adapt to life at the club.
Real Sociedad have been alerted by this, and are believed to be considering a shock deal to lure him to the Anoeta.
To tempt Southampton into letting him leave they are said to be ready to make Vela a part of the deal.
The former Arsenal forward has been a massive hit since signing for the Spanish side, and was a key member of their squad that secured Champions League qualification last season.
The Saints may be tempted by a deal, with the Mexican able to operate on either flank or as a central striker.