The proposals mean RASE would take full control of the Royal Show, Town and Country Festival, Grassland Event and British Pig & Poultry Fair, and Haymarket would take full ownership of the Cereals Event incorporating Sprays and Sprayers.
John Moverley, chief executive of RASE said: "Following a number of strategic reviews, RASE and Haymarket believe that the Society and its many dedicated members, customers, volunteers and visitors would be best served by having independent management of these events.
"In addition, it is the Society's intent to implement an integrated management system seeking to better equip us to meet the specific needs of the sector, both now and in the future.
Dominique Gill, managing director of Haymarket Exhibitions' Land Events said: "We have spent the last two years re-focusing the Royal Show.
"Having ownership of Cereals, a premier event for the arable industry, would expand our exhibitions portfolio and enable us to provide it with the further strategic investment it warrants."
These potential changes will not affect current Society member benefits nor will it affect the scheduling or location of the shows. A decision on whether to go ahead is expected in the coming weeks.