Murray was released from a Los Angeles jail in October after serving two years but wants to clear his name. His attorney had asked the court to overturn his 2011 conviction on the grounds that the intense media coverage of his trial could have influenced the jury.
The cardiologist's attorney, Valerie Wass, said Murray will likely attempt to overturn his conviction in federal court.
"I think that especially with a non-sequestered jury in a high-profile case that's televised, it's impossible to get a fair trial," Wass said, adding that she believes federal courts need to rule on how social media and the Internet can influence a jury.
The trial of Grenada-born Murray, 61, grabbed global attention after Jackson, who was preparing for a series of comeback concerts in London, died unexpectedly in 2009 at age 50 from an overdose of the surgical anesthetic, propofol.
A lower court upheld Murray's conviction in January ruling that there were no errors during his trial.
Murray was convicted after prosecutors successfully argued that the physician was grossly negligent in administering the powerful anesthetic, which was used to help the singer sleep.