A "client’s unilateral belief" in the attorney-client relationship is insufficient to prove privity between the attorney and client, sufficient for a legal malpractice lawsuit, but subsequent behavior or acts by the attorneys might provide the necessary proof.  Here, in Terio v Spodek ;  2009 NY Slip Op 04412
Decided on June 2, 2009 ; Appellate Division, Second Department  we see how that might happen:
 

"To recover damages for legal malpractice, a plaintiff must prove, inter alia, the existence of an attorney-client relationship (see Velasquez v Katz, 42 AD3d 566, 567; Moran v Hurst, 32 AD3d 909; Wei Cheng Chang v Pi, 288 AD2d 378, 380; Volpe v Canfield, 237 AD2d 282, 283). While a plaintiff’s unilateral belief does not confer upon him or her the status of client (see Volpe v Canfield, 237 AD2d at 283), an attorney-client relationship may exist in the absence of a formal retainer agreement (see e.g. Swalg Dev. Corp. v Gaines, 274 AD2d 385, 386). To establish an attorney-client relationship there must be an explicit undertaking to perform a specific task (see Wei Cheng Chang v Pi, 288 AD2d 378; Volpe v Canfield, 237 AD2d at 283).

Here, Reich failed to establish, as a matter of law, that an attorney-client relationship was not formed and did not exist during the time that the alleged acts of negligence occurred. Reich’s submissions demonstrated that it consulted with the plaintiff, advised her of her chances of success, and negotiated a settlement with a bankruptcy trustee. Contrary to Reich’s arguments, the fact that it was purportedly not the attorney of record at the time of a hearing before the United States Bankruptcy Court to determine whether the particular asset at issue qualified as an exemption, is not dispositive of the existence of an attorney-client relationship during the period of the alleged negligence. "