"When we get control we can make sure we get a better balance between EU citizens and those from other parts of the world."
Asked if that meant more or fewer Kiwis being let in, Fox said that would be looked at, "but we want to make sure that there is certainly not less access than there is today".
Fox is visiting both Auckland and Wellington. Tomorrow his schedule includes meetings with Foreign Minister Winston Peters, and Trade Minister David Parker.
When Britain does finally exit the EU - expected to be around March 2019 - New Zealand will require a trade deal with Britain and a separate one for the 27 remaining EU countries.
The New Zealand wine and sheep meat trade into Britain is significant, and New Zealand horticultural products are increasingly making their presence felt in EU markets.
The UK is the second biggest market for New Zealand wine, after the United States, and is worth just under $400 million a year.
New Zealand sends about 200,000 tonnes of sheepmeat to Britain and the EU each year, and Britain remains a significant market for New Zealand lamb.
Fox's trip comes after UK Foreign Secretary Boris Johnson visited New Zealand in July, saying in a press conference that New Zealand was "at or near" the front of the queue for an FTA.