The 26-year-old was a product of the Brest academy before joining Sociedad in 2016, and he has established himself as a key player in the heart of Imanol Alguacil's defence.
Le Normand has played 183 games in the blue and white strip, scoring four goals and providing six assists and winning one Copa del Rey title in the 2019-20 campaign.
Last season, the Spain international made 33 La Liga appearances to help Sociedad achieve Champions League qualification with a fourth-placed finish, and he has played every minute for his side so far this season.
Le Normand - who stands at 6ft 1in tall - was born in France but recently pledged allegiance to Spain, and he won the Nations League with La Roja back in June, playing 78 minutes in the final against Croatia.
The defender has held his place in the Spain backline for their most recent Euro 2024 qualifiers with Georgia and Cyprus, and according to Fichajes, he has attracted glances from Villa.
Lions boss Unai Emery reunited with former Villarreal defender Pau Torres in the West Midlands this term, but he will be working without Tyrone Mings for most of the season due to a serious knee injury.
Diego Carlos, Ezri Konsa, Kortney Hause and Barcelona loanee Clement Lenglet are also at Emery's disposal, but the Spaniard has supposedly earmarked Le Normand as a priority winter target.
Sociedad are in a strong position when it comes to negotiations, though, as the Spaniard remains under contract with the club for another three years, having penned an extension last summer.
However, those terms are believed to include a release clause of €60m (£51.8m), which Villa are supposedly happy to activate in order to bring him to the Premier League.
Sociedad apparently have no desire to negotiate a lower fee for the 26-year-old, who would still have the final say over a move if Villa trigger his buyout clause.
Le Normand would be offered Europa Conference League football with Aston Villa, but Alguacil's side are currently gearing up for their Champions League opener with Inter Milan on Wednesday.
The Spanish side are facing an uphill battle to pip either Inter or Benfica to one of the top two spots in their group, though, while Villa will be expected to progress past AZ Alkmaar, Zrinjski Mostar and Legia Warsaw in their Conference League section.
The Lions have made a satisfactory start to the season with nine points from five Premier League games, but they have already shipped 10 goals in the top flight, with only Burnley and Wolverhampton Wanderers (11 each) holding a worse defensive record.