The north London giants went into the ongoing transfer window looking for two new centre-back additions and they have already signed Clement Lenglet on loan from Barcelona.
Spurs allowed Joe Rodon to leave on loan for Rennes, while they could also see Japhet Tanganga sealing a temporary move away this summer.
Tottenham boss Antonio Conte still wants a new central defender and Spurs have identified Fiorentina man Milenkovic as a potential target.
The Serbian is a man in-demand this summer as Serie A giants Inter and Juventus are also keen on him.
And according to Italian broadcaster Sport Mediaset, Tottenham have held talks with Milenkovic’s agent Fali Ramadani over a swoop for him.
La Viola have slapped a €15m asking price on Milenkovic’s head and want clarity on his future by Friday, amidst interest in his services from both foreign and domestic quarters.
Fiorentina are tipped to tell Milenkovic that he will not leave if he cannot reach an agreement with any of his potential suitors by Friday’s deadline.