The basis for the motion is the alleged breach of the fiduciary duty owed by an attorney to a current or former client. When the law firm targeted by the motion has never represented the moving party, the firm owes no duty to that party. So, in the absence of an attorney-client relationship with the firm, a plaintiff has no standing to bring a motion to disqualify.
HSBC Bank USA, N.A. v. Santos, NY, Slip Op 03976 (1st Dep't July 16, 2020)
Here is the decision.