In response to the fresh leak, a government spokesperson said the UK would forge new and ambitious trade deals but remain an "open and tolerant country" while ensuring there is control of migrants.
Earlier this week, the EU set out what it was prepared to offer the UK, saying it expected the transition to last from the day of the UK's departure on 29 March 2019 to 31 December 2020.
But reports that it could be extended have dismayed some Brexit-supporting MPs.
Speaking during her trade trip to China, Mrs May insisted such an "implementation period" would last about two years.
"We are not talking about something that is going to go on and on...We're leaving the European Union. There is an adjustment period for businesses - and indeed government - for changes that need to be made," she said.
In December, the two sides agreed a deal setting out the rights of EU citizens in the UK and British expats on the continent.
All EU nationals who have been in the UK for more than five years will be expected to be granted settled status, giving them indefinite leave to remain with the same access to public services as now.
Those who have been resident for a shorter period but who arrived before Brexit will be able to stay until they reach the five-year threshold.
At the time, Downing Street said it envisaged anyone arriving after Brexit being able to continue to live, work and study in the UK but that they would need to register and the immigration details would have to be agreed as part of the wider transition negotiations.
The EU has since said it expects existing rules on freedom of movement - including the path to permanent residency - to apply in full until the end of the transition phase.
Mrs May, who is on the second day of a three day trade trip to China, said she would contest the issue of long-term residency rights when transition negotiations begin in earnest next month.
"When we agreed the citizens' rights deal in December we did so on the basis that people who had come to the UK when we were a member of the EU had set up certain expectations," she said.
"It was right that we have made an agreement that ensured they could continue their life in the way they had wanted to - now for those who come after March 2019 that will be different because they will be coming to a UK that they know will be outside the EU."
"I'm clear there is a difference between those people who came prior to us leaving and those who will come when they know the UK is no longer a member."
The BBC's political editor Laura Kuenssberg, who is travelling with the prime minister, said Mrs May was showing she was willing to push back against the EU amid discontent on the Conservative benches.
Labour MP Peter Kyle said anything that caused uncertainty for EU workers in the UK was bad for business.
"EU citizens who come here to work and make an enormous contribution to our country, including in our public services and our NHS, should be welcomed and valued rather than turned away," he said.
In another development, the government's flagship EU (Withdrawal Bill) cleared its first hurdle in the House of Lords as it passed its second reading and former Labour minister Lords Adonis withdrew an amendment calling for a referendum on the final deal.