The 35-year-old was photographed outside Ross Hall Hospital in Glasgow before undergoing a medical on Saturday morning.
The Ivory Coast international could now sign for Celtic before they fly out to Kazakhstan on Monday for their Champions League qualifier against Astana.
The former Manchester City and Arsenal centre-back will be the second signing made by Brendan Rodgers, who brought Touré to Liverpool, since he took over as manager.
Two Celtic central defenders, Jozo Simunovic and Dedryck Boyata, are injured while Efe Ambrose was dropped for the second leg of their victory over Lincoln Red Imps after his mistake cost the Scottish champions a losing goal in Gibraltar.
Celtic have until the evening of Wednesday’s third qualifying round first leg to make one wildcard signing who could feature against Astana.