Foreign students could be forced to leave the UK after their courses finish under new plans being considered by Home Secretary Theresa May.
Most students can currently switch easily from a student visa to a work visa while they are in the UK, but under the new proposals, non-European Union graduates would have to return home and apply for a work visa from abroad if they want to continue living in Britain.
Universities and colleges would also be fined and stripped of their right to sponsor foreign students if they fail to make sure students leave the UK.
May wants to include the plans in the Conservative Party's next manifesto, and a Home Office source told The Sunday Times that she has warned Prime Minister David Cameron that he will be unable to meet his target of reducing net migration if he does not take action on foreign students.
"Making sure immigrants leave Britain at the end of their visa is as important a part of running a fair and efficient immigration system as controlling who comes here in the first place," the source said.
"Theresa is pressing for the next Conservative manifesto to contain a policy that will make sure that anybody coming here on a student visa will have to leave the country in order to apply for a new visa of any kind.
"She wants to make the colleges and universities that sponsor foreign students responsible for ensuring their departure. And she wants to be able to fine colleges and universities with low departure rates and deprive the worst of them of their right to sponsor foreign students."
The plans were criticised by senior Liberal Democrats, who warned that clamping down on foreign students makes "zero economic sense" and would deprive the UK of highly skilled talent.
An aide to Liberal Democrat Deputy Prime Minister Nick Clegg said: "We think it is a very bad idea to get rid of people who have spent years training to be physicists and computer programmers.
"We've invested a lot in these people and to turf them out for the sake of some figures doesn't make any sense."
The proposals could also face a challenge from Chancellor George Osborne, who called on Cameron to abandon quotas for immigrants in a recent speech on EU migration on the grounds that it would have an adverse impact on the economy.
Last month, Cameron said lower EU migration would be a priority in future negotiations over the UK's membership of the EU, and called on EU leaders to support his "reasonable" proposals for far-reaching limits on welfare benefits for migrants.