The differences of opinion peaked last week, when Foreign Secretary Boris Johnson laid out his own Brexit outlook in an article published by the Telegraph on Saturday, which drew criticism from other Tories for promoting key Brexit demands of the opposition.
But the Conservative former chancellor added that Mrs May's lack of a parliamentary majority meant she could not easily dispose of Mr Johnson, who was advised to express his Brexit views in private.
Speaking to BBC Radio 4′s Today programme this morning, Clarke said the only reason Johnson was still in post was because Theresa May was so weak.
Clarke also tore into Johnson for repeating the "simplistic and dishonest" claim made by "hardline leavers" during the referendum campaign that leaving the European Union would allow the United Kingdom to spend an extra £350m on the NHS.
Asked what the PM should do, he replied: 'They should tell him, if he wants to be Foreign Secretary he should actually make some more serious contributions on wider foreign policy, give his views on the Brexit deal privately - as ministers have always been supposed to do - remember there are rules called collective responsibility.
Mr Clarke added: 'In any normal circumstances he'd have been sacked the day after'.
"Sounding off personally in this way is totally unhelpful, and he should not exploit the fact that she has not got a majority in parliament and he knows perfectly well that, although normally a foreign secretary would be sacked instantly for doing that".
'When you're Foreign Secretary, you're a leading member of a government - the foreign policy you propound is the policy of the government, which you've agreed with your colleagues.
But instead, the europhile MP said Johnson knowingly took advantage of the prime minister's weakened position following her poor election performance.
'It's the only sensible, grown-up way to run a government'.
'That's enough of Boris, what we hope is going to emerge is firstly an agreed policy and secondly an explanation to the public'.