The National Restaurant Association said it had not been in contact with the lawyer.
""We have seen media reports that attorney Joel Bennett is publicly making requests on behalf of a former National Restaurant Association employee. Mr. Bennett has not been in contact with the Association. If we are contacted by Mr. Bennett, we will respond as appropriate," association spokeswoman Sue Hensley said in a statement.
Cain, asked in a Fox News interview if he would waive the confidentiality agreement so the woman could respond, said he could not answer yet because of legal implications and the need for consultations with his lawyers.
"I can't answer that right now. It's too soon" he said.
He said he did not think he violated the agreement because he did not mention the woman's name.
Cain acknowledged that a cash payout was made to a woman who filed a harassment claim, after saying on Monday he was not aware of a settlement.
Cain told CNN Headline News that at the time of the claims he did not consider the woman to have received a "settlement" but rather a separation "agreement."
"I didn't change my story. I just simply got the wording right and the difference between settlement and agreement is a difference for me," he said.
Cain said he was only aware of one woman who had made the accusation. News website Politico said there were two.