His efforts have been noted outside of Florence, with interest building ahead of the January transfer window.
Contact has been made from the Red Devils, but no formal offer is on the table.
That is keeping the door open for others, with Juve’s sporting director, Fabio Paratici, among those believed to be closely monitoring Milenkovic.
He has been tracking the youngster since his time at Partizan Belgrade, with it suggested at one stage that the Bianconeri could do a deal before sanctioning a loan switch to aid his development.
Fiorentina have provided that platform in Italy, having completed a swoop in 2017, and have their prized asset tied to a contract through to 2022.
That agreement is allowing Milenkovic to ignore the speculation surrounding his future, with his focus locked on the present.
He is not pushing for a move and his current club have no intention of sanctioning a sale.
Juve, though, may test the transfer water as defensive reinforcements become more of a priority.
Goal has revealed that there are no plans to part with Medhi Benatia and Daniele Rugani over the winter, but both men are sparking exit talk.
Ajax star Matthijs de Ligt had been the Bianconeri’s favoured option to bolster the ranks, but the Dutchman may prove too costly.
As a result, Milenkovic has registered on the radar in Turin.
Juve will get another look at a player they hold in high regard on Saturday, with Massimiliano Allegri’s reigning champions due at Stadio Artemio Franchi for their latest Serie A outing.