Due to the curbs, many international students have reportedly been deterred from considering Britain as a destination to study.
Some universities have reported a fall in applications from India but the actual figures will be known later this year when the academic session begins.
As education and industry leaders petitioned Cameron with figures that international students bring 8 billion pounds annually to the British economy, The Sunday Times quoted a source at 10 Downing Street as saying, "The Prime Minister understands these arguments and is definitely considering a change of policy".
Immigration minister Damian Green has been using falling numbers of student visas granted (62 per cent drop in student visas in the first quarter of 2012) as evidence that the Cameron government is on course to deliver its election pledge to reduce net immigration from 'hundreds of thousands to tens of thousands'.
Green has consistently rejected arguments that international students should not be counted in net immigration figures because most of them return to their countries at the end of their studies.
Students comprise the largest category of migrants to UK.
One of the changes that has reportedly put off Indian students is the closure of the post-study work visa in April, which allowed self-financing students to recover some of the cost of studying here by working for two years after their course is over.
Those calling for international students not to be included in net immigration figures include Business Secretary Vince Cable and Universities minister David Willetts, besides the Universities UK, the organisations representing higher education institutions in the UK.
In a jointly-written article in The Sunday Times, Conservative MP Nadhim Zahawi and Labour MP Paul Blomfield, warn of a "growing perception abroad that, in terms of higher education, Britain is not open for business".
Zahawi and Blomfield write, "Recent changes to the student visa system have unfortunately broadcast the message that foreign students are unwelcome.
"We've already seen a dramatic fall in students coming from traditional markets such as India".
They add, "Taking students out of the net migration targets would enable us to look again at the changes that have been introduced.
"It could, for example, provide a basis for reviewing the restrictive rules on post-study work, which is a key issue for many students who are keen to consolidate their learning in the country of study.
"Above all it would send out a positive message to prospective students throughout the world you are welcome in the UK".