Despite the English Premier League transfer window closing on August 31, clubs in Turkey have until midnight on the September 5 to conclude all late deals.
Galatasaray's interest in the defender was sparked when stalwart Tomas Ujfalusi was ruled out for up to four months after collapsing during training, and Terim feels Toure's former Arsenal team-mate Emmanuel Eboue, who plies his trade at Turk Telekom Arena, might be able to help them in their pursuit of the 31-year-old.
"We have to bring someone (in). Obviously a defender," Terim told reporters.
"We're interested in Kolo Toure from Manchester City. We can ask help from Eboue if we need.
"We have to complete this transfer until UEFA Champions League list deadline."
The Premier League champions' business on transfer deadline day suggests Toure could be surplus to requirements, with Roberto Mancini having moved for defenders Maicon and Matija Nastasic.