Matt Hancock has refused to rule out banning students from returning home at Christmas, to limit the spread of coronavirus outbreaks.
The health secretary was responding to a question about concerns that students could be spreading Covid-19, amid numerous university-based outbreaks.
At Glasgow University 120 students have tested positive for Covid-19 and are among 600 self-isolating there.
Academics had warned against the mass movement of the UK's million students.
The University and College Union had called for students to be taught wholly online, from home until Christmas, ahead of the start of term, but ministers advised some face-to-face learning was key to students' mental health.
This has meant up to a million students have returned to their university premises or are commuting there regularly.
- In a response to a question on BBC Radio 4's Today Programme about whether students would be asked to stay in their university towns at Christmas, Mr Hancock said he had "learned not to rule things out".
"I don't want to have a situation like that and I very much hope we can avoid it.
"We have said throughout that our goal is to suppress the virus, whilst protecting the economy and protecting education.
"And protecting people in education whether it's school or university is obviously critical as is protecting the economy."
He added: "In terms of universities, we are working very closely with them to try to make sure the students are safe, but that they can also get their education."
"I've learned not to rule things out and one of the challenges that we have is how to make sure people are as safe as possible."
But he added: "This is not our goal, I don't want to leave you with the expectation - but we have to work on all contingencies at the moment."
It comes after a growing number of outbreaks on university campuses, with students isolating in their residential groups at Glasgow, Dundee and Liverpool.
Boris Johnson has said universities have been given a "clear request not to send students home in the event of an outbreak, so as to avoid spreading the virus across the country".
Socialising
University students are being urged not to hold parties in their halls of residence under the rule of six, and to avoid socialising in places that do not have Covid-19 protections in place.
Many universities are warning students they face fines or even having their courses terminated if they do not follow the regulations.
Universities have taken extensive measures in their buildings to minimise risks on campuses and many lectures are already being taught online, but there is less control over what takes place off university premises.
But minutes of a recent meeting of the government's scientific advisory group on emergencies, suggest ministers were aware of the risks of bringing students back to university and sending them home at the end of term.
The minutes of the 1 September meeting said: "Sage noted that risks of larger outbreaks spilling over from HE institutions are more likely to occur towards the end of the academic term, coinciding with Christmas and New Year period when students return home.
"This could pose risk to both local communities and families, and will require national oversight, monitoring and decision-making."
UCU general secretary Jo Grady has said the evidence was clear that online learning should be the default position and that government should be working to prevent outbreaks not creating conditions for them.
She said:" students and their parents will be rightly worried about being locked down in an unfamiliar area over Christmas.
"Locking students down at Christmas is based on a flawed boarding school vision of university that ignores the fact thousands of students and staff commute every day around the UK to and from university.
"Threatening to lock students up over the festive period is not the solution."
She also urged the government to act now, before thousands more students move onto campuses this weekend.
It was completely irresponsible to let students go back to university when outbreaks have already started, she added.
'Number one priority'
University leaders say they have working hard for months to ensure students can return to their campuses safely.
"Ensuring the health, safety and wellbeing of students, staff and local communities in the new academic year is the number one priority for universities," said a Universities UK spokeswoman.
UUK said institutions were taking action to encourage responsible student behaviour, would continue to follow the latest government and public health advice, and were working in partnership with local authorities and public health bodies "to ensure that effective and rapid outbreak response plans are in place and clearly understood".
