Giakoumakis is prepared to move on from Celtic this month amid a lack of starts handed to him by Hoops boss Ange Postecoglou.
However, Japanese club Urawa have taken a big step forward towards signing the striker as they have an agreement with Celtic.
It is claimed the package would be worth €4m to Celtic.
Giakoumakis would be able to sign a lucrative contract if he chooses to continue his career in Japan.
However, other sides have still not given up in the race for the Greece international and MLS side Atlanta are pushing for him.
Giakoumakis came off the bench in Celtic’s Scottish League Cup semi-final on Saturday and hit the back of the net.