As of Wednesday morning, the day before clearing opens, there were more than 27,000 courses listed on the Ucas clearing website, according to a Press Association survey.
The figures come the day before sixth-formers across England, Wales and Northern Ireland receive their A-level grades and learn if they have achieved the results they need to secure their university places.
This year there has been a drop in applications to start degree courses at UK universities this autumn, fuelled by factors including a fall in the 18 and 19-year-old population, changes to funding for nursing degrees and the possible impact of Brexit.
The fall, coupled with reforms which mean universities are no longer restricted by a cap on student numbers, means many institutions which still want to fill places are entering clearing in a bid to attract and recruit qualified candidates.
Clearing is the annual process that matches students without places, for example those that did not meet their required grades, with available courses.
The Press Association's survey, based on 148 UK universities and colleges, shows that around nine in 10 institutions (132) are advertising at least one course on the Ucas clearing website.
In total, there are more 27,715 courses listed that potentially have availability.
It is understood that a number of universities list all of their courses on the site ahead of results day, even if they are expected to be filled with students already given offers, until those offers are confirmed on Thursday.
Among the 24 Russell Group institutions alone, those universities considered among the best in the country, two-thirds (16) had at least one course listed on the Ucas site, with 4,820 courses potentially having places on offer.
Jessica Cole, Russell Group head of policy, said institutions "want to attract talented and able students from all backgrounds".
"If a student does go into clearing, we know it can be a nerve-wracking time," she said.
"But it's important to remember that all our universities have people on hand to help, as do Ucas.
"Some have places to offer to students who have exceeded expectations, and some have places for highly-qualified students who have narrowly missed out on their first choice."
The survey also found that the majority of universities and colleges, about 79% in total, are advertising clearing on their own websites.
Last year, almost 65,000 applicants found places through clearing, while almost 900 were placed through "adjustment", a scheme that allows applicants that do better than expected in their A-levels to trade up to another course or institution.
Overall, 649,700 people had applied to start degree courses by June 30, the last deadline for applications, down around 4% (down 25,190) compared with this point last year, Ucas figures show.
Those applying after the end of June do so through clearing.
A breakdown shows a 4% decrease in UK applicants, while the number of EU students planning to study at a UK university or college has fallen by 5%.
There has been a 2% rise in international students from countries outside the EU.
The proportion of 18-year-olds in England applying to universities has reached a new high, with 37.9% planning to study for a degree, up from 37.2% in 2016.
Alistair Jarvis, chief executive of Universities UK, said there is still "great demand" for places.
"There are a variety of reasons for the drop in applications this year, including the decline in the number of 18 and 19-year-olds, changes to funding for degrees in nursing, and the possible impact of the vote to leave the EU.
"There will still be more applications than there are university places."
Under funding reforms, bursaries for nursing students have been scrapped and replaced by loans.