"A proposal will be put to ministers shortly and, if approved, it's likely an advert will be placed in July and interviews held in September," said a government spokesman.
Acting commissioner Maria Battle said that although elections had slowed the political process, the commission's work has carried on. She said.
"Peter's last words to us were, 'Take the work forward'."
Asked if she would like the job of commissioner, Ms Battle, a solicitor and specialist in children's issues, said she couldn't comment."
One of Mr Clarke's main priorities was a national schools counselling service.