Capital punishment has been on hold in Kentucky since a 2010 injunction.
Coleman and Gov. Andy Beshear have been at odds over whether the former can sign a death warrant. One objection cited by the governor deals with obtaining the chemicals necessary to perform a lethal injection.
In March, Coleman told members of the media that pathways were now in place to access those chemicals.
"President Trump signed an executive order early in his administration ordering the U.S. Department of Justice to assist states like ours to obtain those medications," he said. "Also, within the last year, year and a half, there have been executions just north of the river in Indiana, lawful executions. The state of Indiana has been able to obtain these medications. Other states have."
The failed Tennessee execution comes a week after the Kentucky Supreme Court found that Beshear's concerns about the lack of execution drugs were valid and refused to lift the injunction, halting executions.
The high court has allowed a suit challenging the state's execution protocols to move forward. Among other issues, that suit raises concerns about lethal injection drugs and their administration.
Meanwhile, Tennessee's failed execution of Krista Pike was called off after she was given two doses of the drug meant to kill her. The failure led Gov. Bill Lee to postpone Tennessee's lone remaining execution this year and to order a review.