The 33 year old left Celtic in August and is a free agent after a spell in the USA.
Nolan played with Cole at West Ham and said his ex-team-mate, who won seven England caps, is a "great lad".
"We have had a chat. It would be fantastic if I could bring him over," Nolan told BBC Nottingham Sport.
"The best thing is to see if he is interested and we can work something out. He has a few things in the fire.
"He will be a breath of fresh air. He is a top pro and a good player. If we can make it happen and the embargo gets lifted, then we will try our best to do that."