Reports from Italy have suggested are closing in on the 18-year-old midfielder, although Bayer Leverkusen are also interested.
City are already looking for the successor to Micah Richards, a Manchester United target, and one of the candidates is the Greek teenager.
Their intention to offer 4million euros for Papadopoulos will be very welcome by Olympiakos at this stage.
Papadopoulos has a contract with the Reds until next summer, but he will not renew it despite Olympiakos' calls for a new deal, as he anticipates the interest of major European clubs.
In view of that the Piraeus club are considering selling this summer so as to avoid losing him for free next year, says www.sportingreece.com.
Leverkusen are also reported to be keeping an eye on Papadopoulos, but they are yet to make their move.