A source close to the Education Secretary said: "Michael Gove thinks Theresa May is a superb Home Secretary.
"We will continue to work well with the Home Office and other government departments to combat extremism in all its forms.
Ofsted will publish their findings next week and Peter Clarke will publish his report in July."
More top news
Several people are thought to have been killed in a fire at a traveller's site in the Republic of Ireland.
More than 90% of hospices in England have been rated 'good' or 'outstanding' in a wave of new inspections.
Britain's youngest MP in 350 years said that the Commons still has a 'boys club atmosphere' which is 'alive and well'.