Blues boss Aitor Karanka is keen to add to his firepower for the second half of the season and his side have failed with an offer for Hibernian’s Kevin Nisbet.
Hibs are not willing to sell the 23-year-old and Birmingham have switched their attention to Greek hitman Giakoumakis.
The 26-year-old is on the books at Dutch club VVV-Venlo and has taken the Eredivisie by storm this season.
Giakoumakis has hit 21 goals in just 20 Eredivisie games, as well as scoring twice in a single cup tie.
He hit four goals against Vitesse earlier this month and was again on the scoresheet against Fortuna Sittard at the weekend.
Birmingham are claimed to have shown they are willing to meet VVV-Venlo’s asking price of between €4m and €5m for the Greek hitman.
However, the striker is at present minded to spend the season in the Netherlands.
A number of Premier League sides are tracking the hitman and is determined not to be rushed into a move.
And with the clock ticking in the transfer window, Birmingham may have a mountain to climb to sign him.