While Savic struggled during a one-year spell at Manchester City in 2011-12, the centre-back has since impressed at Fiorentina and Atletico.
However, having featured in less than half of his side's La Liga and Champions League matches this season, it appears that an exit during the next window could be a possibility.
According to Todofichajes, the Montenegro international is interested in signing for Spurs, who may look to replace Jan Vertonghen.
Although it has been suggested that the North London outfit would prefer to focus on free agents, a chance to sign Savic for a reported fee of £13.5m may prove too tempting to turn down.
The 29-year-old has a contract at Wanda Metropolitano until 2022.