In his BBC interview, Johnson said the President's social media spat with May was "probably misinterpreted".
"While there may be disagreements of how he said something, or how he does something, I think you can be rest assured that the security and prosperity. are top of mind to him".
But he said the leaders still had a "very very good relationship" and he believed the visit would still happen.
The ambassador acknowledged that Trump had raised hackles in the UK.
Meanwhile, Labour MP Stella Creasy said welcoming Mr Trump to Britain effectively told women victims of sexual abuse that "they don't matter". The president had not yet set a date for the possible visit, he added.
"It is protecting Americans here and the US". It's protecting Americans here and the US. That's number one and that's my number one as well and so if you look at it in the context of that, that is what he is trying to do. "He's not going to go down the path of a lot of politicians and be namby-pamby about it".
"After the latest incident - where President Trump used Twitter to promote a vile, extremist group that exists exclusively to sow division and hatred in our country - it is clear that any official visit here would not be welcomed".
"He is going to come out, he is going to probably take some chances, in an effort to do that, to accomplish that security goal and maybe he will ruffle feathers". Speaking of May's visit to the Oval Office in January, Johnson said: "The prime minister was his first visitor, the first official foreign leader to visit".
After a Downing Street spokesman said he had been wrong to do so, the president hit back, telling May to focus on "destructive" terrorism in the UK.
Johnson said he was hopeful about the prospects of a visit.
Any visit by Trump to the United Kingdom would likely be met with large-scale protests.