The Greek striker was denied an introduction off the bench against Raith Rovers last week after suffering an injury while warming up.
But the former VVV-Venlo striker, who was the top scorer in the Eredivisie last season, is set to give Ange Postecoglou some much-needed reinforcements up front.
Celtic dropped more points in the cinch Premiership on Sunday when they were held to a 1-1 draw by Dundee United at Parkhead with centre-forward Albian Ajeti missing a glorious chance by blazing well over from three yards.
When asked about Giakoumakis, the Celtic manager said: "The scan came back actually more positive than we thought so we're hoping he'll get back into training this week, which is good news because he's missed a fair bit.
"It wasn't just the injury which we thought might be significant. We thought he might have to go back into rehab.
"But the fact the scan has come back pretty good means he can get back out training again."
Although Celtic's Europa League clash with Bayer Leverkusen will come too soon for the striker on Thursday, Postecoglou is hopeful he could feature at Aberdeen on Sunday.
"He only really missed two days of training and had a session (on Sunday)," Postecoglou added. "Hopefully he'll be back training with the group early in the week."
The former Australia head coach saw his injury issues mount further when Josip Juranovic (tight hamstring) and James McCarthy (knock) suffered first-half injuries against United.