Sunjic, 26, left Russian side Kuban Krasnodar in August, making the move to Germany in order to replace new Roma signing Antonio Rudiger at Stuttgart.
The defender has made a strong start to life in the Bundesliga, scoring on his debut against Hertha Berlin in a 2-1 defeat - and whilst he only made his move to Stuttgart last month, interest in his services remain.
Tutto Mercato Web report that Aston Villa are tracking Sunjic, but could face competition from Premier League rivals Bournemouth and Everton.
Any move from Villa for Sunjic would be a surprise considering that manager Tim Sherwood moved to bring in five defenders over the summer, landing Micah Richards, Joleon Lescott, Tiago Ilori, Jose Crespo and Jordan Amavi.
Yet with Ilori only on loan from Liverpool, Sunjic may be a future target in case they can't sign him permanently, but a move to Everton may be more likely.
With his international team-mate Muhamed Besic already at Goodison Park, Sunjic may be tempted by a move to Merseyside, with Roberto Martinez still needing defensive reinforcements even after signing Ramiro Funes Mori from River Plate.
Sunjic surely won't leave Stuttgart in January, and right now, the Premier League clubs are only monitoring his progress in Germany ahead of any possible future move for the player.