That’s according to former Hoops hitman Frank McAvennie, speaking exclusively to Football Insider about a new “problem” at the club.
Giakoumakis, 26, has started two of Celtic’s last three Premiership games.
Furuhashi made way for the Greece international as the Hoops drew 0-0 with Livingston on Saturday.
Jota and Furuhashi have been in electric form this season, bagging 13 goals between them.
However, McAvennie claims the decision to start Giakoumakis in recent weeks could lead to better performances from the Hoops’ usual attackers.
“Postecoglou has such a headache now,” McAvennie told Football Insider correspondent Ben Wild.
“That’s a great thing in a way. You would rather have too many players to choose from than not enough.
“But if all of the attackers are scoring, someone is going to be annoyed.
“There are always a lot of games when you are in Europe so every player should get a chance.
“The issues come in the big games, like the Old Firm, or a cup final. Then you find out who the manager really prefers.
“That can lead to new problems but it can also inspire the other players to improve and impress.
“I’m glad Giakoumakis is finally getting a go. That extra competition up front will benefit Kyogo and Jota.”
He netted 26 goals in 30 outings during last season’s Eredivisie campaign.