The move from Downing Street is part of a drive to woo Labour Brexiteers ahead of the critical vote in the Commons next week on the prime minister's deal.
According to the Daily Mirror, the fresh amendment would keep EU rules on pay and conditions, health and safety issues, plus environmental standards.
It has been tabled by the Labour MP John Mann, and has the backing of his colleagues Gareth Snell, Caroline Flint and Lisa Nandy.
At a Westminster briefing, Ms May's spokesperson said of the amendment: "In terms of that specific amendment, if it is chosen that is something we would consider very seriously.”
Mr Mann said that government backing for the proposal could make the PM's plan "more attractive".
"If we have a guarantee that works on workers' rights and conditions, that's significant," he said.
But the move was dismissed by Frances O'Grady, the general secretary of the Trade Union Congress (TUC), who said: "The PM has talked a big game on workers' rights all along, but once again the reality falls short. This isn't the binding, long-term guarantee that working people want."
John McDonnell, the shadow chancellor, said the TUC had exposed the "con on workers' rights" that Ms May is "trying to perpetrate".
"Nobody's fooled," he said. "May is just desperately trying to hang on. It's increasingly evident that there is no government in power so let's have the general election that the country needs to sort this out."
Labour MP Mary Creagh - a supporter of the People's Vote campaign - added that there "is no possibility of a 'better Brexit' that can protect workers' rights or the environment".
She added: "We were told repeatedly that the government's deal was the best possible deal Britain can get, so to suggest that the deal can now be renegotiated with the EU again is yet more fantasy have-your-cake-and-eat-it politics."
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