The 24-year-old has been linked with prominent clubs since January and several of them are now getting serious.
Marseille have been keen on Giannoulis since the winter and have returned for him. The French club ‘intend to make a move’ for Giannoulis, it is reported.
They face competition from Premier League side Newcastle, who have entered the running.
The Magpies want to build a strong team and have enough money to satisfy PAOK’s demands.
Sportime reports that the offers PAOK have received so far have been worth up to €3.5m. PAOK rejected those and want €5-6m to part with Giannoulis.
PAOK face Besiktas in a Champions League 2nd round qualifier on Tuesday and there may be developments after that.