The Ivory Coast centre-back has struggled to earn a regular first-team place under Roberto Mancini, who further bolstered his defence with the signing of Matija Nastajic last week.
The arrival of Nastajic is likely to push Toure further down the pecking order at City, and he is now a top target for the Turkish side ahead of their transfer deadline day on Wednesday.
His former Arsenal team-mate Emmanuel Eboue signed for Galatasary in August last year, and Terim believes he could play a key role in persuading Toure to follow him.
"We have to bring someone in, obviously a defender," said Terim.
"We're interested in Kolo Toure from Manchester City. We can ask for help from Eboue if we need.
"We have to complete this transfer by Wednesday, which is UEFA's Champions League list deadline."
Source: team talk
Source: team talk