Durham University is offering students who delay their studies until next year a financial incentive.
The university said it had "capacity issues" due to the "unprecedented situation" after a U-turn in A Level results, the BBC reports.
Following a backlash over results, the government announced that grades would be revised and would instead be based on teacher-assessed grades.
However, this meant many students missed out on a university place due to their initial grades.
And due to the university not being able to provide enough spaces they said "it is possible some offer holders" will have to enrol in 2021.
Students who defer for a year will receive a bursary and a guarantee of accommodation- although it is not yet known how much the bursaries would be worth.
The university would "seek volunteers" and offer the incentives "to help with their transition to university life" next year to "minimise" the number of people affected.
Students were unable to sit exams due to the coronavirus pandemic and received A Level results based partly on the predictions of their teachers but modified by a computer algorithm which led to nearly four in ten results being downgraded.
Ofqual announced the A Level grading change after days of outrage from students, teachers and MPs across the country, with many demanding a U-turn from the Government.
It came after similar announcements in Wales and Scotland with Northern Ireland following the same route.
Education Secretary Gavin Williamson apologised to students for "the distress this has caused" following the announcement of the Government's U-turn.
After the changes were announced, students tried to reclaim spots at university after being rejected just days before.
The government said it will work closely with universities to help them through this period of change.
