May is will deliver a high profile speech on Brexit in Florence on Friday. Saturday's controversial Daily Telegraph article was aimed at sending a signal he could not support such a relationship.
"Hopefully, that happy circumstance will follow the speech the prime minister is due to give on the subject in Florence on Friday".
Johnson was piqued that a meeting of other senior ministers involved in Brexit was held last week when he was inspecting hurricane damage in the Caribbean.
Johnson and May are both in NY for the UN General Assembly, but it was reported that they have not met since his article was published, despite staying in the same hotel.
Asked whether Mr Johnson should be sacked, the Prime Minister replied: "Boris is doing good work as Foreign Secretary".More news: WWE Raw: Brock Lesnar, Braun Strowman have tense interview
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"I will be seeing Boris at various stages during our time here, but of course we have got very busy programmes".
"The cabinet is absolutely clear about the destination we are aiming for in relation to our European negotiations".
If Britain remains in the single market, it would continue to pay for access and would need to abide by European Union rules and regulations, including freedom of movement. He wrote his 4,000-word manifesto, he said, because he believed it was time people heard what he had to say on Brexit.
He said: 'We are working together, that is the key thing, to make sure that Britain can take advantage of the opportunities of Brexit'.
It is understood that May's speech will avoid discussing the finer details of a future UK-EU relationship, which would leave the door open for either of the options reportedly favoured by different members of the cabinet.
Boris Johnson has insisted he will not be resigning from the cabinet over #Brexit but said he hoped the prime minister would avoid hitching the United Kingdom too closely to the European Union after its departure.
"So I contributed a small article to the pages of the Telegraph, and now everyone who had previously accused me of saying too little are now saying I am saying rather too much", he said. The article was published without Downing Street's approval.
Veteran Tory Europhile Ken Clarke said Mr Johnson should have faced the sack for his Brexit intervention, while fellow grandee Lord Hague issued a call for Cabinet unity.