The Hoops are keen to strengthen their frontline before the transfer window slams shut and have identified the Greece international as an ideal candidate.
Having zeroed in on Giakoumakis as their target to bolster their strike force, Celtic are said to have opened negotiations over a deal for the centre-forward.
It is said that Celtic manager Ange Postecoglou also phoned Giakoumakis personally in an attempt to convince him of a move to Parkhead this summer.
While Giakoumakis was claimed to be impressed with Postecoglou’s approach, he prefers a move to 2. Bundesliga club Werder Bremen, according to Dutch daily De Telegraaf.
The 26-year-old, who recently revealed that he has several offers on his table, has even made a secret visit to Werder Bremen to discuss a potential transfer.
However, the German second division club are struggling to reach an agreement with VVV-Venlo over the transfer fees for the former AEK Athens frontman.
Celtic, though, are prepared to offer the Dutch outfit a fee of €3m, which is closer to their asking price of €3.5m.
Werder Bremen though are hopeful that Giakoumakis desire to move to Germany will help them strike a deal with VVV-Venlo soon.