The reigning Premier League champions are understood to have already opened negotiations with the Greece international's current club, Schalke, and are close to reaching agreement over a move when the transfer window reopens on July 1.
Roberto Mancini has identified the 21-year-old as a player that can strengthen his back line, with Joleon Lescott and Kolo Toure both linked with Etihad Stadium exits this summer.
Lescott has fallen behind Matija Nastasic in the first-team pecking order while Toure is out of contract at the end of the season, meaning Vincent Kompany will be the only other recognised centre-back alongside Nastasic, should both players move on.
Manchester City will face competition for Papadopoulos's signature, though, with local rivals Manchester United also believed to be monitoring his development in the Bundesliga.
Sir Alex Ferguson might look to bring the Schalke star to Old Trafford as he continues his search for a long-term replacement for Rio Ferdinand, while there are some doubts that still remain over the long-term fitness of Nemanja Vidic.
Papadopolous is under contract in Germany until 2016, but with a £17million buy-out clause written into his existing deal, both Manchester City and Manchester United know the size of fee it will take to activate a direct transfer tussle.
AC Milan have also been mooted as potential admirers of the Greek defender, who has been capped 16 times by his country, though a big-money move to the Premier League looks like the most likely option.