The attorneys for Richard Glossip and two other death row inmates said they plan to file for a stay of execution.
Glossip is set to die on Jan. 29, but it will not take place if the Supreme Court gives at least five votes for the stay.
Back in 1998, Glossip was sentenced to death for the 1997 murder of Barry Van Treese.
The other death row inmates set to die are John Grant on Feb. 19, and Benjamin Cole's execution is planned for March 5.
Oklahoma executed convicted murderer Charles Warner after the Supreme Court denied Warner's stay with a 5-4 vote.
But those four votes were just enough for the court to grant a review.
On the night of Jan.15 the attorneys for Charles Warner did not received what they requested.
But a week after Warner's execution, the challenge filed by attorneys for three other death row inmates, including attorney Dale Baich, will be heard at the nation's highest court.
"Since it last addressed the issue in 2008 the landscape has changed significantly," said Dale Baich, one of the attorneys for the three death row inmates.
In 2008, in the case of Baze vs. Rees, the court ruled a particular three-drug lethal injection cocktail did not violate the Eighth Amendment of cruel and unusual punishment.
The initial drugs purpose was to put the inmate in a deep, coma-like unconsciousness.
But the availability of that drug has lessened, so states such as Oklahoma and Florida began to use the drug midazolam as the initial drug.
In Supreme Court documents the questions that seek answers will focus on the use of midazolam.
Defendants argued the drug cannot maintain a deep, coma-like unconsciousness and the state selected midazolam because of availability, rather than to create a more humane execution.
But in a released statement Attorney General Scott Pruitt stated Oklahoma's three-drug cocktail has "successfully been implemented" and the state "will continue to defend the (protocol's) constitutionality."
Baich and his team said they will now request stays of execution until a Supreme Court ruling is made.
"We're happy the court is going to take another look at these issues," said Baich.
Oral arguments are set to begin April 29 and the case now references death row inmate Richard Glossip as the main defendant.
His execution is scheduled for this Thursday.