The Parkhead club have been looking to land the VVV-Venlo hitman for the past couple of weeks and have been duking it out with Werder Bremen.
The Greek international finished last season as top goalscorer in the Eredivisie despite his club stuttering their way towards relegations.
It is believed Celtic manager Ange Postecoglou has already had a telephone conversation with the player as he mapped out how he sees the 26-year-old fitting into his system.
Giakoumakis was also said to have met officials from Bremen in person but, according to the Daily Record, that potential move is now dead in the water after the Bundesliga II side refused to meet the forward’s wage demands.
Similar reports have surfaced in Germany and the Netherlands, which state Celtic are now set to snap up the player for around £2.5 million.