Judge Sherry Stephens did not rule on the request during a status conference Thursday morning. The next hearing is set for July 18.
Juan Martinez, the prosecutor, maintained that the retrial should be held on schedule for this summer and said he hoped to find a jury by then.
Arias' attorneys had planned to call witnesses to the stand last month, but withdrew, saying the convicted murderer's friend was receiving death threats. The attorneys have asked to move the retrial until January 2014 to give them time to find witnesses for the sentencing.
Arias was found guilty of first-degree murder May 8 in the 2008 stabbing and shooting death of her then-boyfriend Travis Alexander in his Phoenix home.
The jury that found her guilty could not make a decision on whether Arias should be sentenced with life in prison or the death penalty. Under Arizona law, a hung jury in the death penalty phase of a trial requires the selection of a new jury.
If that jury cannot come to a decision, Arias will automatically get life in prison. From there, the judge would decide whether Arias would get life without parole or life with potential parole eligibility after 25 years.
Regardless, Arias' murder conviction will stand. A new jury may take weeks to select, and from there the court will hold a mini-case to get the jury up to speed on the case thus far.