Qatari Emir Shiekh Tamim bin Hamad Al Thani visited Downing Street to meet Theresa May last week, at which point the pair agreed to explore ways to build on investment, education, science and research and defence.
And today, Fox has begun a visit to both Qatar and the United Arab Emirates, which will include both meetings with senior government officials and a roundtable for Qatari investors into the UK.
Speaking in Dubai today, Fox said the UK had already prioritised 31 “big-ticket” exporting opportunities across the Gulf region.
“This not only covers traditional industries such as oil and gas or defence and infrastructure, but emerging areas like life sciences and creative,” Fox said.
A spokesman for the Department of International Trade said Fox would hold informal talks with Qatar's ruling powers.
“This is all building up relations for when we do actually leave and we are in a position to start signing things,” they said, adding that UK exports to Qatar grew 16 per cent in 2015.
"It's a strong growth market for us," they said.
It comes after officials in Number 10 pledged the UK would not defy EU rules which preclude talks with other countries, and in particular those with which Europe is currently negotiating.
“Whilst we remain a member of the EU, we will comply fully with our responsibilities,” a Downing Street spokesman said.