Milenkovic, 23, has been heavily linked with a move to United following recent reports from La Repubblica (as relayed by Calciomercato).
The highly-rated Serbian defender has emerged as one of Europe’s most commanding centre-backs.
It has been the Serbian’s continued impressive form which has seen him linked with a move to some of the Premier League’s biggest clubs.
The latest in the ongoing saga comes from Italian outlet Gazzetta dello Sport (via Sports Witness), who claim that alongside United are now Pep Guardiola’s Citizens also chasing the Serbian.
GDS also go on to report that Milenkovic has been a long-standing target for United, dating back to the days of Jose Mourinho.
In terms of how much the 23-year-old could cost, a figure of around £30m is considered to be enough to prize him away from Italy.
It is not yet known which Manchester club are leading the race to land Milenkovic, however, with both clubs rumoured to be in the market for a new defender, the summer transfer window could really heat-up.