Celtic are set to play the first leg of their tie against Astana tomorrow.
Celtic have the option of naming one player in their team who they have not yet registered for the tie.
Toure only signed for Celtic at the start of the week, but Brendan Rodgers’ side are short of options in central-defence.
Although it looks most likely that Mikael Lustig and Erik Sviatchenko will continue at the back, Davies has suggested that Toure has a chance of featuring in the second leg of the fixture.
“We will see how we go and how Kolo does with his fitness this week,” Davies said.
“For now, we are focusing on what we have.”
Toure is due to link up with his new Celtic teammates when they return from Kazakhstan later this week.
Celtic are set to face Astana in the first leg of their Champions League tomorrow evening.
The Bhoys made it to this stage by beating Lincoln Red Imps from Gibraltar 3-1 on aggregate.
Celtic have not qualified for the Champions League in two years, and they are desperate to do so this time around.