Michelle Lyons, a spokeswoman for the Texas Department of Criminal Justice, said that Jose Ernesto Medellin, 33, could be put to death by midnight, CNN reported. He had been scheduled to die by lethal injection at 6 p.m.
Medellin's lawyers say that he was denied access to a Mexican consul when he was arrested for participating in the rape and killing of two teenage girls.
The execution was put on hold when the Supreme Court decided to consider a request for a stay, McClatchy Newspapers reported.
The Texas Parole Board rejected a request Monday for a stay or commutation of sentence.
Prison officials moved Medellin to a cell next to the death chamber in Huntsville Monday night.
The Medellin case has created an international debate because Medellin was not granted access to the Mexican Consulate after his arrest -- a violation of international law. The Mexican government, the United Nations and the Bush administration have all called on Texas to halt the execution and review his case and that of four other condemned Mexican nationals in U.S. prisons; however, a U.S. Supreme Court decision has backed up the state's decision to proceed.
Medellin was one of six members of a Houston gang convicted of the crime. A co-defendant was executed in 2006.