The lawyer, Nareg Gourjian, had worked on Michael Jackson's child molestation defense.
Murray, who is charged with involuntary manslaughter in the death of Michael Jackson, wants Gourjian to replace Joseph Low, who left the defense team earlier this month.
Gourjian's former law firm, headed by lawyer Mark Geragos, raised the possible conflict of interest before Los Angeles County Superior Court Judge Michael Pastor at a hearing Tuesday.
"We have a great amount of respect for Mr. Gourjian, but it is our duty to disclose his participation in our past representation for Mr. Jackson," Geragos and Geragos attorney Pat Harris said.
The Geragos firm represented Jackson for two years starting in 2003, when he was charged with child molestation. Jackson replaced Geragos with Thomas Mesereau in 2004, saying he wanted an attorney who would devote his full time to his case.
Geragos was also defending Scott Peterson, who was charged with murdering his wife, at the same time.
Gourjian told the judge he was "in no way inolved" in the Jackson case because he was "a brand-new lawyer" busy working on the Scott Peterson murder case at the time.
The decision rests on if Gourjian's work for Jackson was "substantially related" to the current case and if his work for the defense would require "Gourjian to attempt to discredit his former client directly or indirectly," Pastor said.
The judge delayed a decision until more facts are provided by Geragos and there is a response from the lawyer for Michael Jackson's estate.
Mark Geragos will be asked to appear at the next hearing on February 24, the judge said.
Murray is also represented by Houston lawyer Ed Chernoff and J. Michael Flanagan of Los Angeles.
The defense demanded a speedy trial at last month's arraignment, the trial to start by the end of March. Jury selection is now set for March 24.