According to reports in Greece, there is a €150k-a-year gap (roughly £2,500 per week) in the wage demands from the striker and what Celtic wish to pay.
Sportime editor Giannis Chorianopoulos reports a deal of €3m has been agreed with VVV-Venlo for the 26-year-old.
Celtic manager Ange Postecoglou is already said to have held discussions with the player about his role in the team for the forthcoming season.
Giakoumakis was the leading scorer in the Eredivisie last season despite his club being relegated to the second tier of Dutch football.
If Celtic can get the deal over the line, Giakoumakis would become the tenth signing of the summer after the additions of Kyogo Furuhashi, Carl Starfelt, Liel Abada, Josip Juranovic, Joe Hart, Liam Shaw, Osaze Urhoghide, Joey Dawson and James McCarthy.