31-year-old Cole, who is a free agent, has been training with the Hoops but is yet to be offered a contract by the Scottish champions.
Lustig said: "I don't think he has played for a little while, but you can still see he's a good player.
"He's experienced and he looks very good in the box.
"He's done really well down south and he brings us something that we don't have right now.
"He's a box player and is maybe stronger in the air. You always want new additions that can make the playing squad better.
"If we do sign Carlton, then it's not going to make us worse – we will be better."
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