The Greek hitman has found his opportunities limited at Celtic so far this season, despite many feeling he has impressed when given the chance.
Giakoumakis has grabbed eight goals in 25 outings for the Bhoys this term, but his future may be away from Celtic.
Inside Futbol understand that Giakoumakis’ agent is looking at a number of options which would see him depart Glasgow.
The striker would be keen to test himself in the Premier League and would welcome a switch south of the border.
Giakoumakis would also be open to Germany and Italy as destinations.
Celtic paid a fee of £2.5m to sign Giakoumakis from Dutch side VVV Venlo in the summer of 2021.
He picked up the Scottish Premiership title and the Scottish League Cup with Celtic last season and it remains to be seen if he will still be at Parkhead beyond January to add to his Bhoys trophy collection.