In a speech, he will question whether institutions are attracting the best students - with only half of student visas issued for university courses.
Home Office research suggests a fifth of students are still in the UK five years after being granted visas.
But the National Union of Students dismissed Mr Green's comments as a "misinterpretation" of the facts.
The Home Office study tracked non-EU migrants who came to the UK in 2004. The largest group - some 185,000 people - were students, and 21% were still in the country five years later.
BBC home affairs correspondent Danny Shaw says this, together with an increasing number of new overseas students, has led Mr Green to make reform of the student immigration route a priority.
'Out of control'Ministers also intend to examine work visas as two-fifths of people in this group remained in the UK after five years.
Ahead of his speech, Mr Green said: "We can't assume that everyone coming here has skills the UK workforce cannot offer".
He told BBC Radio 4's Today programme: "I don't want to interfere with the success stories of our universities".
BBC News
