Steven Armstrong said he was "still confident" a tariff-free frictionless trade deal would be done.
But he told the BBC that a no-deal outcome would "force us to think about what our future investment strategy for the UK would be".
Mr Armstrong said a deal based on the EU-Canada deal would not work for Ford.
Although a similar UK-Canada arrangement "would allow tariff-free trade, it would still involve border checks - and would upset the just-in-time delivery model used by the company in Europe", he said.
In the UK, Ford makes engines at its plants in Dagenham and Bridgend. It also has a joint venture making gearboxes in Halewood on Merseyside.
His comments come as Prime Minister Theresa May prepares for a crucial Brexit summit on Wednesday amid fears that talks have hit a "real problem" over the Northern Ireland border.
Mr Armstrong said he would not like to see a Brexit that meant the UK would default to World Trade Organization rules and tariffs. "That would put a significant amount of cost in our business," he said, adding that any additional costs would make the UK less competitive.
"It would certainly make us think long and hard about our future investment strategy."
Ford's Bridgend plant is losing its contract to supply engines for Jaguar Land Rover (JLR) in 2020, and the plant is seen as vulnerable.
Mr Armstrong said there was an investment strategy for Bridgend for the near-term future, and that plan would continue.
But beyond that, "it very much depends on what happens post-Brexit", he added.
"If we have a deal that allows us to be competitive in the UK then we will continue with the investment strategy. But it's too early to be specific about Bridgend at this point."
He dismissed suggestions that Brexit could be a convenient excuse to shrink the Bridgend plant after the JLR contract ends: "We have to look at what's happening within our broader business. We have been very clear since [JLR] decided to put their business elsewhere that we would continue to look for options for Bridgend."
source: BBC News
Ford's European boss has said a no-deal Brexit "would be pretty disastrous" for British industry and could affect the company's future in the UK.