Ministers are reportedly considering plans to limit benefits for new immigrants and give multi-year visas to migrant workers in key sectors as part of efforts to stick to the pledge to bring net inward migration down to the tens of thousands.
The plans being discussed by senior ministers could also see the independent Migration Advisory Committee (MAC) advising the Government on how many visas should be issued to take the political sting out of the issue, according to The Sunday Times.
Under the proposals for a post-Brexit Britain with full control over immigration, new arrivals could be given five-year working visas if they have a job but be banned from claiming any benefits during that time.
The MAC would decide how many visas need to be issued for workers in key industries such as software engineering, health and social care, farming and hospitality, which are heavily reliant on immigrants.
The Prime Minister reportedly ordered ministers to make preparations for a new system at a meeting of the Cabinet's Brexit committee on Thursday.
According to the newspaper, Mrs May will also attempt to guarantee the rights of all EU nationals who are resident in the UK on the day she triggers Article 50 to begin exit negotiations, if she can get a similar agreement for British expats in Europe.
This is because Home Office lawyers have warned the Government would face a legal challenge if it made the cut-off date the day of last year's EU referendum, June 23, the report said.
A Government spokesman said: "We said we would use the opportunity of leaving the European Union to take control of our immigration system and we will do exactly that.
"Our plans will be published in due course but this is just speculation."