The Daily Telegraph is reporting that Mr Johnson is prepared to walk out of the Cabinet if the Prime Minister concedes too much to Brussels when she delivers a major speech in Florence on Friday.
But allies of the Foreign Secretary dismissed the report as "mischief".
Mr Johnson, in New York for the United Nations General Assembly, said: "We are working together, that is the key thing, to make sure that Britain can take advantage of the opportunities of Brexit."
And asked directly if he would resign, he replied: "No."
The prominent Leave campaigner spoke to TV cameras in New York after bumping into them at a hotel lift as he returned from a jog.
It comes amid reports of Cabinet infighting over Britain's divorce from the EU.
The Foreign Secretary denied claims of a split, saying: "We are a nest of singing birds."
Mr Johnson has been accused of "back-seat driving" the Brexit talks after he published a 4,000-word article setting out his vision for a clean-break Brexit and the UK's future outside the EU.
The article was seen as an attempt to undermine the PM, but the Foreign Secretary has
dismissed any such claims, saying "there is one driver in this car - it's Theresa".
The Prime Minister also tried to reassert herself, saying: "This Government is
Mr Johnson and Mrs May are both in New York, but no formal meeting between the two is planned.
The Cabinet is due to be briefed on Thursday on Mrs May's Brexit plans.
Reports say a rift in the Cabinet centres around the approach to Brexit, with ministers such as Chancellor Philip Hammond favouring Swiss-style payments for continued participation in the single market, while others, including Mr Johnson and Michael Gove, are believed to prefer a deal involving a free-trade agreement similar to the one between the EU and Canada.
Earlier, former foreign secretary William Hague
called on Mrs May to unite her Cabinet around a Brexit strategy in her speech this week.
If she fails to unite the Government, he wrote in the Telegraph, the Tories might lose power and "Jeremy Corbyn will be Prime Minister".
Source : https://news.sky.com/story/brexit-boris-johnson-denies-plan-to-quit-over-differences-with-pm-11043212Thanks you for read my article Boris Johnson Denies Plan To Quit Over Brexit Differences With PM