The Greek international has been in fine form this term, notching an incredible 14 goals in 14 games so far.
His razor-sharp displays have alerted a number of European sides, with Liverpool and Arsenal at the front of the queue along with Dortmund.
The trio are all considering January bids for the 25-year-old, who is likely to cost around £7m.
Liverpool are thought to be looking at providing star strike duo Luis Suarez and Daniel Sturridge with some support, and see Mitroglou as a good option.
Meanwhile, Arsene Wenger wants to further boost his Arsenal side’s title push by adding another source of goals to his squad.
Dortmund are also keen as they look to replace the soon to be out of contract Robert Lewandowski.
Mitroglou has spent time away from Olympiacos on loan in recent years, but has managed to force his way into the first-team squad in recent times.
With Greece still in the running for World Cup qualification, the hit-man may be keen to make a high profile move in the New Year to boost his chances of making the trip to Brazil next year.
Should Arsenal or Liverpool move for Kostas Mitroglou?
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