Johnson, who has vowed to take Britain out of the European Union at the end of October with or without a deal, is due to hold talks with several European leaders in New York including Germany's Angela Merkel and Irish Prime Minister Leo Varadkar.
He will also discuss progress on reaching a Brexit deal with European Council President Donald Tusk.
"I would caution you all not to think that this is going to be the moment," he told reporters on the plane on the way to New York. "I don’t wish to elevate excessively the belief that there will be a New York breakthrough."
Johnson said that while a "great deal" of progress had been made since he took office in July as EU leaders now acknowledged the Withdrawal Agreement reached with his predecessor needed to be changed, there were "clearly still gaps and still difficulties".
He wants to remove the so-called backstop, an insurance policy aimed at avoiding a hard border on the island of Ireland by having Britain follow the bloc's rules on trade, state aid, labor and environmental standards so no checks are necessary.
Last week Britain shared technical documents with Brussels setting out its ideas for dealing with the contentious issue of the backstop, although these were not the formal legal proposals Brussels has asked for.
Johnson has said he wants to secure an amended deal at an EU summit on Oct. 17-18, and said "a large number of the important players", including Britain, Germany, France and Ireland wanted to reach an agreement, Reuters reported.
"We have seen interest in the idea of treating the island of Ireland as a single zone for sanitary and phytosanitary purposes that is also encouraging," he said. "However there are clearly still gaps and still difficulties."
Johnson said it was important the United Kingdom "whole and entire" was able to diverge from EU law in future.
"The problem with ... the current backstop is that it would prevent the UK from diverging over a huge range of industrial standards and others," he said. "We may want to regulate differently but clearly there is also a strong incentive to keep goods moving fluidly and we think we can do both."