Hunt also tweeted: "The BBC understands there is no cause for concern regarding the health of either the Queen or Prince Philip".
He has also reported that the staff meeting will take place at 10am.
The rumours began after reports emerged of an emergency meeting being called for Buckingham Palace staff from around the country. They are expected to gather at the palace mid-morning.
The BBC report that these meetings take place once a year.
"The Queen met Prime Minister Theresa May on Wednesday to formally agree the dissolution of parliament ahead of the general election, while Prince Philip attended Lord's Cricket Ground to open a new stand."