According to Mundo Deportivo, Spurs could attempt to bring Savic to the Tottenham Hotspur Stadium during this summer's transfer window.
The 29-year-old has been an important player for Atletico since arriving from Fiorentina in 2015, making over 150 appearances in all competitions.
Savic's contract with Diego Simeone's side is due to expire in two years, though, and it is alleged that an offer in the region of €20m (£18m) would be considered by the Spanish giants.
The Montenegro international represented Manchester City between 2011 and 2012, featuring on 11 occasions in the Premier League before joining Fiorentina. body check tags ::