The Sunday Times reported the Business Secretary, who represents Tunbridge Wells, could be one of a dozen ministers on the Prime Minister’s ‘suicide watch’.
Mr Clark was named part of the remain-supporting ‘Breakfast Club’ minister group, who may be liable to resign.
It was reported that should Theresa May lose her Brexit vote, the group would press for a new referendum.
Mr Clark said: “I meet with groups of MPs as part of my job. I strongly support the Prime Minister.”