But universities could not offer places to students who did not apply, he told a vice-chancellors' conference.
So partnerships between universities and schools may have a key role.
Mr Denham told the meeting in Leicester: "No-one could seriously argue that the current social bias across higher education and in individual institutions - including some of the most sought after - reflects a system that reaches all of our most talented young people."
The government was removing the financial barriers to studying by providing more generous grants and bursaries, he said.
And much had been done to encourage universities to consider all the factors indicating a student's ability to succeed.
Participation had broadened and deepened with a steady increase in the numbers of students from low income families going to university, he said.
But he added: "Even the most talented must be sufficiently well prepared to study and succeed.
"So university partnerships with schools will become ever more important - to help schools deliver the high standards we want and to identify and nurture the young students of the future."
