The BBC said the discussions are expected to focus on "providing certainty, continuity and increasing confidence for UK and US businesses as the UK leaves the EU".
Fox pointed out, "the 'UK-US trade and investment' working group is the means to ensure we get to know each other's issues and identify areas where we can work together to strengthen trade and investment ties."
The British Chambers of Commerce (BCC) director general Adam Marshall said the US's experience at such negotiations would make it difficult for the UK to secure a good deal.
"We're just getting back into the game of doing this sort of thing after 40 years of doing it via the EU," Marshall said.
"So I think early on in the process, it would be concerning if the UK were to go up against the US on a complex and difficult negotiation."
Trade unions, the TUC and Unite, have also expressed unease over a rushed US trade deal.
"Ministers should be focused on getting the best possible deal with the EU, rather than leaping into bed with Donald Trump," TUC boss Frances O'Grady told the media.
But independent economist Michael Hughes told the BBC's World Business Report that talking to the US at this stage was important. "To have some preliminary ides and get some basic principles out is a sensible thing to do," he believes.
Earlier this month, US President Donald Trump said he expected a "powerful" trade deal with the UK to be completed "very quickly". At the time, a UK government official said President Trump and UK Prime Minister Theresa May had agreed to prioritize work on a post-Brexit trade deal.
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