Public schools Eton and Winchester have refused to comment on claims they are seeking an immunity deal in an inquiry into an alleged conspiracy to inflate fees.
Eton is under investigation by the Office of Fair Trading
According to the Times newspaper, both colleges have been offered a "supergrass" deal to reveal details to the Office of Fair Trading (OFT) about an alleged cartel among fee-paying schools.
Eton College in Berkshire and Winchester College in Hampshire both deny breaking the law on anti-competitive practice.
Public and independent schools across the country have imposed a record real-terms increase this year in fees, averaging more than 9% - four times the rate of inflation.
But that reflects an unusual set of cost pressures this year arising mainly from changes to teachers' pay and pension arrangements and national insurance contributions - the same factors that have caused a crisis in so many state schools.
In a statement, Eton College's bursar Andrew Wynn told BBC News Online: "All the matters reported in the Times are being discussed in full co-operation with the Office of Fair Trading and we do not feel it appropriate to comment at the moment other than to that office."
A Winchester College spokesman told BBC News Online: "The college is working closely with the OFT and will not be commenting on this matter in any way until the OFT has completed its deliberations."
The Times said the two colleges had brokered a deal with the OFT to avoid paying millions of pounds in fines in return for assisting the inquiry.
The OFT can grant immunity or partial exemption from fines for parties which co-operate with its investigations.
The scale of this depends on the stage of the inquiry when the approach was made, a spokesperson said.
The Independent Schools Council Information Service said on Monday that it was aware that a small number of its member schools - fewer than half a dozen - were co-operating with the OFT.
At the time the inquiry had begun they had not believed they were doing anything unfair or prohibited, a spokesman said.
"We await the outcome of the OFT's deliberations."
Pupils at all-male Eton, which was founded in 1440 by King Henry VI, pay annual boarding fees of more than £19,000.
The college, which has 1,290 boys aged between 13 and 18, has came top in this year's private schools GCSE results league tables.
Winchester College was established 600 years ago and has 700 boys and 100 teaching staff.
It has retained its position at the top of the private schools' A-level league tables.
Winchester students averaged just under four As in their A-levels this year.