Deputy Vice Chancellor Peter Jimack said the university was making the offer as some courses were full.
He said the nature of teacher-assessed grades as opposed to exam-based grades had made it "harder to predict" the number of successful applicants.
Prof Jimack told the BBC: "We've contacted students on a small number of programmes in two schools to let them know that we are going to make them an offer to defer to next year with an incentive of a cash payment of about £10,000 and our fee for their halls of residence in their first year being paid by the university.
"We are not putting pressure on anybody to make that choice, it's an entirely free choice."
He said any students who chose to defer until 2022 would be provided with online materials to help them prepare for their arrival next year.
He added that the university was also creating an extra 30 places to study medicine for students who were unable to get a place at universities which were oversubscribed.
A record number of students have applied to study medicine this autumn, a rise of more than 20% on last year.
The number of places for medicine in England is capped by the government.
Prof Jimack said: "We recognise that there is a national need and we know from the last 18 months how important our doctors and nurses are.
"So we're stepping-up and making available some additional places that we will make available to students from oversubscribed universities to come and study with us at Leeds."