Trump will become the US' 45th President on 20 January, and Farage said the incoming administration will be keen to stress its commitment to the principles of global trade.
"I am absolutely certain, knowing not just Trump, but many of the Trump team, they want to show the outside world that they are not protectionist," Farage said on Sky News this morning.
"They're worried about trade with places like China. Where state subsidy is closing down steel production in America, or we could even argue South Wales, come to that. But when it comes to countries that are equivalent, they are open to doing business.
"I suspect within the first few months of a Trump presidency, there will be a big statement from [Trump commerce secretary nomination] Wilbur Ross, or someone like that, saying 'we want to do this'," Farage said, adding that he expects the US government to stress: "We want to get this done in three months."
"Then it's going to be up to the British government to respond to it," Farage said.
Farage is one of the few UK politicians to have met Trump since the US election last November, with the President-elect later arguing that the former Ukip leader would be a desirable candidate for the UK's ambassador to Washington.
Theresa May's government is restricted from entering into formal talks over trade deals with non-EU members ahead of Brexit.
However, there have been increasing calls for May to quit the EU's customs union and focus on trade with nations outside of Europe.
And only last week, New Zealand prime minister Bill English indicated his own desire to secure a free trade deal with the UK.
More broadly, the former Ukip leader also said he had yet to be convinced by the Prime Minister's response to last summer's referendum.
“I'm quite certain Theresa May will do what she always does – sound very reassuring. She will look to be very much in control, saying all the right things and people like me will say it sounds great, but why is it taking so long?” Farage said.
“When it comes to immigration, in particular, which she is highlighting, this is coming from the person who was home secretary and failed completely. I'm yet to be convinced, I have to say.”