School director Dr Claire Matthewson said it seemed the eventual final course enrolments would exceed last year's final 2166 figure and would also top the overall school record of 2199 in 2006.
The equivalent enrolment at a similar stage last year was 2346, which later dropped to the final 2166 figure after students cut the number of papers they were studying.
Students can study one or two papers.
"We're clearly on the right side of the fence," Dr Matthewson said.
About 1950 students had enrolled yesterday for the university's ninth annual school - also well up on 1680 last year.
Organisers said that the first morning of the latest school had been the busiest in the school's history.
Dr Matthewson warned that the provisional enrolment figures needed to be interpreted cautiously, because the final figure would be reduced by some students deciding to take fewer papers.
However, the likely outcome remained positive.
It was unclear why enrolments had risen so much, but including information about the school in a mail-out of final semester academic results for the first time last year may have contributed, she said.
The school offers students the chance to gain academic credit for six-week courses which usually take 13 weeks to study during the main academic year.
Seventy-seven papers are being offered this year, down slightly from a record 78 last year.
Organisers said the 28 new papers which were being offered this year were enjoying mixed fortunes in initial popularity.
A new third-year-level politics paper on "news media and international crises" was proving popular, with 46 enrolments.
A new botany paper, on identifying New Zealand plants, had also attracted considerable interest, with 19 enrolments.
Among the school's happiest participants are about 20 US students from Dartmouth College, a leading university in New Hampshire.
Ellie Chapman said they were enjoying the contrast between snowy, subzero conditions in the American winter and summer temperatures in Dunedin.