After his telephone conversation with the Foreign Minister, Dr Fox tweeted saying, "Great to talk to Bangladesh Foreign Minister."
He said it was very much a meeting of "minds on the need for a more effective and dynamic" WTO.
On July 8, the United Kingdom nominated Dr Liam Fox for the post of WTO Director-General to succeed Roberto Azevêdo.
A Former minister and leading Brexiteer, Liam Fox remains in the running to be the new head of the World Trade Organization.
Three other contenders have been knocked out of the competition after failing to secure enough votes. It means five candidates are there in the race to be the next director-general.
Fox would be the first British boss of the organisation, which regulates the terms of international trade.
British Prime Minister Boris Johnson tweeted his congratulations to Fox, saying the WTO "would be in excellent hands under his leadership."
He has also won the support of his ministerial successor. Trade Secretary Liz Truss said she was "delighted" Fox remains in the race.
The second phase of consultations will run until October 6.
During this time, members will be asked in confidential consultations to express two preferences to the facilitators with an eye to bringing the number of candidates from five to two, according to WTO.
Following this process, another Heads of Delegations meeting will be called at which the results will be announced to the WTO membership.
The timetable for the third and final round of consultations will be announced at that time.