The broadcaster could seek the sums from Sky and Virgin Media, despite their refusal to meet similar requests from the BBC and ITV.
Communications Minister Denis Naughten is conducting a review of broadcasting legislation and could force the fees introduction.
The Irish Independent has been given sight of a report commissioned by RTE from Mathew Horsman’s Mediatique.
Based on subscriber numbers Sky could pay €19 million and Virgin €11 million. In a survey 49% of respondents said they would leave Sky if it did not carry the Irish public broadcaster. 63% said they would leave the cable service.
The report itself was completed at the end of 2014.
In July 2017, UK broadcasters ITV and Channel 4 were told they shouldn’t expect to receive retransmission fees from platforms carrying their services. The Digital Economy Bill closed a clause in Section 73 of the Copyright, Designs and Patents Act, which prevented the collection of retrans fees.