Almost 5,000 foreign migrants granted visas to study in the UK each year could be refused entry under new powers to weed out bogus students, figures suggested on Monday.
The Sun reported a Number 10 source saying the prime minister was "definitely considering a change of policy."
The Home Office said on Monday they would bring in risk-based interviews of up to one in 20 potential international students following a successful pilot scheme, the Home Office said.
UK Border Agency (UKBA) staff will also be given a new power to refuse entry to any applicant whose credibility they doubt, with potential students from India, Bangladesh and Burma expected to be among those hardest hit.
The three-month pilot scheme found 32% of almost 2,000 students from outside the EU who were interviewed and granted a UK visa would have been denied one if UKBA officials had the power to refuse visas because they suspected the applicant was not a genuine student, the Home Office said.
Almost half (45%) of applicants from Burma would have been refused under the credibility test, along with almost two-fifths (38%) from Bangladesh and almost a third (29%) from India, the pilot scheme which ran from December last year to February found.
Between 10,000 and 14,000 student visa applicants - around 5% of the total - are expected to be interviewed over the next year.
Further new powers will also enable officials to refuse a visa to anyone who fails to attend an interview without a reasonable explanation.
Immigration Minister Damian Green said: "With more interviews and greater powers to refuse bogus students we will weed out abuse and protect the UK from those looking to play the system."
He went on: "Under the current system UK Border Agency officers are unable to refuse some applications even if they have serious concerns over the credibility of the student.
"We are toughening up the system to keep out the fraudulent and unqualified while ensuring genuine students benefit from our country's excellent education sector."
Mr Green added: "Britain is open for business to the brightest and the best migrants but the message is clear - if you lie on your application form or try to hide your true motivation for coming to the UK then you will be found out and refused a visa."
High-risk applicants will be identified and asked a number of questions about their immigration and education history, study and post-study plans, and financial circumstances following the pilot scheme, the Home Office said.
Some 2,300 students from 47 nations were interviewed at 13 overseas posts in a bid to test how effective face-to-face interviews and the new refusal powers would be.
Around a fifth (17%) were refused entry, with language problems being the main issues in one in four (24%) cases, the Home Office said.
Some were unable to answer even basic questions in English without the aid of an interpreter, despite claiming to have good enough language skills to study at higher and further education institutions in the UK.
Officials were also concerned over the legitimacy of some 32% of the rest, with 60% of these claiming to want to study at a private higher or further education college and 14% at a university.
If the same proportion of the 14,000 students interviewed over the coming year were refused, study visas could be denied to some 4,620 applicants.
The risk-based interviews will be brought in ahead of the expected summer surge in student applications and will focus on those countries where abuse is suspected of being most prevalent, the Home Office said.
Based on the results of the pilot scheme, these could include India, Pakistan, Bangladesh, Sri Lanka, Burma, Nigeria and the Philippines.
But students from low-risk countries such as Australia, Canada, Hong Kong, Singapore and the USA - which already use a streamlined application process - will be exempt from the "genuine student" test.