The on-loan Arsenal star joined the Gunners back in August 2011 - but is yet to make an appearance for Arsene Wenger's side.
Campbell, who can play in midfield or as a striker, has been shipped out to Lorient, Real Betis and Olympiakos since joining Arsenal for an undisclosed fee.
The 21-year-old has scored five goals in 14 games in the Greek Super League so far this season - with Campbell often playing off the right wing.
Campbell could further adhere himself to the Arsenal faithful if he can help Olympiakos knock Manchester United out.
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