Groups representing small shareholders argue they should be involved in ensuring good corporate governance.
Investors hope RBS will serve as a test case so other companies will consider installing a shareholder committee.
RBS said it had not seen full details but pledged to "look closely" at it once it had.
The way companies are managed - and how much bosses are paid - has been been under particular scrutiny this year following the collapse and loss of 11,000 jobs at BHS and the revelations about pay and working conditions at Sports Direct.
Chief executives of FTSE 100 companies have a median pay package of Â£4.3m, according to the High Pay Centre, which works out at 140 times that of the average worker.
In November, the government issued a Green Paper to explore improving how companies are run.
It proposed that a shareholder committee could be set up "to scrutinise remuneration and other key corporate issues such as long term strategy and directors' appointments".
The UK Individual Shareholders' Society (ShareSoc) and the UK Shareholders' Association (UKSA), who represent retail (individual) investors, said: "We suggest that this initiative will significantly benefit corporate governance at RBS, and represents a valuable opportunity for RBS to lead the way in exploring a concept which works well in other countries."
ShareSoc and UKSA will present RBS with a resolution for the proposal to be included on the agenda at the bank's annual general meeting in May, where investors would then be given the chance to vote on the measure.
A spokesman for RBS, said: "We have not yet received the final draft resolution. Once it has been delivered we will look closely to ensure that it complies with all corporate governance and listing guidelines."
Small investors in RBS are pushing for the bank to set up a shareholder committee to give them a bigger say in areas such as executive pay.