UK defence secretary Michael Fallon told BBC: "This is not going to happen".
But he said firms could be asked "simply to report their numbers".
A row broke out after a briefing note was distributed following UK home secretary Amber Rudd's speech to the Conservative Party conference last week which seemed to indicate that all firms will be asked to reveal the exact number of non-British workers they employ.
"What I can absolutely rule out is that we will not be asking companies to list or publish or name or identify in any way the number of foreign workers they have," Fallon said.
"We're going to consult with business, and the consultation document hasn't even been published yet, on how we can do more encourage companies - to incentivise them - to look first at the British labour market. And to offer these jobs to British people, which is what the British people would expect, before they import labour more cheaply from abroad," he said.
"That would mean, for example, asking companies just simply to report their numbers, which we wouldn't publish, we wouldn't identify anybody," he clarified.
UK education secretary Justine Greening also told ITV the policy was "about collecting the right evidence if we are going to be able to respond to skills shortages... This is not data that will be published, there will be absolutely no naming and shaming".
"The Tories anti-foreigner agenda is a distraction from their own complete failures of policy, and against the best interests of society... We need answers from the Tories on how they will protect our economy, but they have no plan other than a risky hard Brexit which would threat our prosperity.
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