Talks will hopefully take place soon
The International Trade Secretary also hopes "within the next few weeks" to start talks directly with his US government counterpart once that person had been appointed and confirmed in office.
The early contacts between his department and the new US administration come after Theresa May and Mr Trump discussed last Friday in the White House their hopes for a swift post-Brexit trade deal.
Dr Fox told the Commons' International Trade Committee that while Britain remained in the European Union it would abide by membership obligations which ban us from signing trade deals with other parties.
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Dr Fox said Mr Trump made clear to Mrs May that he wants a free trade deal
The more good news we give to the public the better
"However, it would be against Britain's national interest for us not to be discussing with future trade partners what those arrangements might be that the UK would want to have in the future," he said.
His department would take legal advice as matters proceeded over how far it could go in talks.
Dr Fox said Mr Trump made clear to Mrs May that he wants a free trade deal with the UK once we leave the EU.
Civil servants from Dr Fox's department will be in Washington next week to explore the "scope and ambition" for a deal.
Setting out other preparations for Britain's global trade after Brexit, Dr Fox told MPs that discussions were already underway with countries including Australia, China, India, New Zealand, South Korea, Turkey and Gulf States.
He rejected criticism his department's recent trumpeting of £16billion invested in the UK since last June's EU referendum was largely based on decisions unveiled before that vote.
"It was an antidote to the idea that people are not going to be investing in the UK," said the Leave campaigner.
"The more good news we give to the public the better - and it counters some of the black propaganda that comes from some who want to undermine the referendum."
Mexico Wall: Trump gives the go ahead Thu, January 26, 2017
The structures, fences and walls that mark the border between the United States and Mexico as President Donald Trump reiterates his promise to build a wall along the U.S. border with Mexico.
AFP/Getty Images 1 of 11
Combo with images of the border fence between Mexico and the U.S. taken in the states of Sonora and Baja California, Mexico, and in the states of Arizona and California, U.S., between July 2, 2016 and January 25, 2017.
The earlier contacts with the departments came when Mrs May met Mr Trump
He forecast big new announcements at the Qatar trade and investment conference in London and Birmingham in March/next month.
"We already have in our pockets, as it were, some good investment announcements that will be made. They’re well into the billions range but we're not going to announce them until we get there," said Dr Fox, whose department was set up by Mrs May last year to promote foreign investment into the UK and British investment and exports overseas.
He insisted the Government could hit its target of boosting the value British exports to £1trillion a year - but it was "unlikely" to be reached by the 2020 deadline.
Dr Fox also added that discussions at the World Trade Organisation confirmed that Britain should be able to move smoothly “with no turbulence and no vacuum” at Brexit to new arrangements, initially based on the current trade tariffs the EU puts on non-European countries.
Fox said that it would be against Britain's best interests not to discuss with trade partners
The hearing also heard of work to build up Britain's team of trade negotiators, after 44 years in which the EU has conducted all trade deals on the UK's and other members’ behalf.
The trade policy team of 40 in the old Business Department has grown to 180 people in Dr Fox's ministry, and is set to rise to over 350 by 2018, top civil servant Sir Martin Donnelly told the MPs.
The department has been taking advice from "friendly countries" including Australia, New Zealand, Canada and Singapore "about what a 21st Century trade negotiating team looks like".
The Government has also set up a trade policy negotiation training unit where staff are getting tips from international experts, said Sir Martin: "We're confident we're building the expertise we need to run really effective trade negotiations."
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