Mr Bannon said the President gave the Prime Minister advice to get the best Brexit deal when she visited the White House in January last year.
He also gave her a copy of his book “The Art of the Deal”.
Mr Bannon said: “Trump gave her some pointers and pulled her off to the side and said, ‘Hey if I was doing this here is how tough you have got to be because these guys are not going to let you go’.
“He gave her the précis of his book ‘The Art of the Deal’ which is ‘overshoot your target, be tough and get on with it – because if this drags on it is going to be bad’.”
The US President hinted he had told Mrs May how to deal with the EU earlier this week when in an interview with the Sun he said the Conservative leader had ignored his advice on negotiations.
Mr Bannon also lambasted Mrs May’s Brexit paper published earlier this week and questioned her leadership.
He said: “Theresa May has got a lot of great qualities – I am not sure if it is the right leader at the right time”.
Mr Bannon also sang Boris Johnson’s praises for his resignation letter.
He said the white paper was “the flood tide, the moment” for the Brexiteer to act.
Mr Bannon seemed to suggest Mr Johnson could lead the country, saying: “I believe moments come. It is like Donald Trump, people dismissed him.
“Now is the moment. If Boris Johnson looks at this.
“There comes an inflection point, the Chequers deal was an inflection point, we will have to see what happens.”
He said the former Foreign Secretary is “one of the most dynamic people on the world stage”.
He added: “I’ve always found incredibly engaging. He’s a big ideas guy. I believe he looks like a doer.
“For someone who was foreign secretary to actually resign over this, I thought his [resignation] letter was terrific.”
“People respond to bold action, the bold action can have hard edges on it, and the bold action doesn’t have to be perfect, it can be a little shabby some times.”