Thompson also said the prosecutor had treated his client, Nafissatou Diallo, more like a defendant than a victim, according to the report.
"Ms Diallo wants Dominique Strauss-Kahn to be held accountable to the fullest extent under the law, both in criminal and in civil court," the newspaper quoted Thompson as saying on Sunday.
"She should not have her right to go to trial in a criminal case taken away by the Manhattan district attorney's office."
According to legal experts, Thompson's motion will almost certainly fail because under the law his client has no authority to ask for Vance's office to be replaced by a special prosecutor, the paper noted.
"It's what we call an AOD: an act of desperation," the newspaper quoted Stephen Gillers, a professor at New York University Law School, as saying.
"She may benefit from a successful prosecution, but she has no legal interest in the prosecution."