Nissan had pledged to manufacture the new SUV model in the UK four months after the referendum - a move seen as a major vote of confidence in the country's manufacturing outside the EU.
The news casts doubt over Nissan's future investment in the UK, and stokes debate about the future of British car manufacturing less than eight weeks before the UK is scheduled to leave the European Union.
Many Remain supporters said the withdrawal was a worrying indicator of Brexit having a corrosive impact on the British economy.
Liberal Democrat leader Sir Vince Cable said Nissan's withdrawal could be a turning point in Brexit uncertainty, and said it showed that big companies were "very seriously reconsidering their future here".
Sir Vince added: "The whole industry is rethinking its approach because it originally saw Britain as a gateway to Europe and that gateway is now closing.
"I think Brexit is a major factor, it may be one of several. Not just for Nissan but the same calculations are being made throughout the car industry."
Shadow Brexit secretary Sir Keir Starmer said the withdrawal, if confirmed, "represents a serious blow to the communities that depend on the jobs Nissan creates and supports".
He said the Conservatives' "chaotic handling" of negotiations was having a "devastating impact on business investment".
Julie Elliot, the Labour MP for Sunderland, said she would ask the government to intervene to protect jobs in the city.
"But we cannot deny the inevitable role that Brexit plays," she continued. "The constant uncertainty, the chaotic government. None of it is conducive to encouraging business investment in this country."
Ms Elliot urged constituents to await an official announcement from Nissan, however.
Conservative pro-Remain MP Anna Soubry said it was "difficult not to be angry" that the manufacturer may pull production.
Unite's assistant general secretary for manufacturing, Steve Turner, said it was "beyond disappointing" that Unite members heard about their futures and the holding back of planned Sunderland investments through the media and not directly from the company.
"These rumours are disturbing and will cause the workforce to have a very anxious weekend even though production of the X-Trail would have necessitated additional jobs on site," he said.
In the 2016 referendum, Sunderland voted 61.3% to leave the EU.
As of Sunday morning pro-Brexit MPs remained largely silent regarding the news.
Asked more generally about Brexit negotiations by Sky News' Sophy Ridge, International Trade Secretary Dr Liam Fox said there was "increasing worry" about the European and global economy.
"We've seen a big slowdown in China, it's had a knock-on effect," he said.
"We've seen Italy now go into recession, we've seen the German economy slow down, we've seen the French economy slow down. Really we do need to avoid any disruption to that European trading system."
He said the priority was to talk to European partners to "see if we can get an agreement and get an agreement as quickly as possible".
Nissan employs roughly 7,000 people in Sunderland, and was thrust into the heart of the Brexit debate in 2016 when it received a letter from government ministers offering undisclosed reassurances about the company's future competitiveness.
Four months after the referendum, the Japanese carmaker said it would build its next-generation Qashqai sports utility vehicle and a new X-Trail model in Sunderland.
The X-Trail is currently produced exclusively in Japan.