"I think we've got a good chance, a good chance, of being able to dispense with one-meter plus," Johnson told reporters during a local election campaign visit to the north of England.
Johnson struck a cautious tone ahead of the planned easing of foreign travel restrictions.
"We do want to do some opening up on May the 17th, but I don't think that the people of this country want to see an influx of disease from anywhere else. I certainly don't. We've got to be very, very tough, and we've got to be as cautious as we can," he said.
While campaigning, Johnson has faced questions about who paid for the refurbishment of his apartment and childcare for his young son.
He declined to comment on the allegations during his visit to Hartlepool.
"All this kind of stuff is absolutely not relevant," he said, adding that voters wanted to focus on policies ahead of the elections on Thursday (May 6).
Leader of the British opposition Labour party, Keir Starmer, welcomed reports that some senior members of Johnson's Conservative party were recognising the implications of breaching ministerial code.
"Over the last week or so, some people have said... holding the prime minister to account is somehow party politics. This demonstrates that it isn't, there's a shared cross-party need to uphold standards in public office. And I think other senior Conservatives should follow suit now," he said on Monday.