The show is likely to be in late June, before Hampton Court and after BBC Gardeners' World Live, which the RHS pulled out of this month.
Hampton Court will be a week later in 2016, in early July. The RHS's late July Tatton Park show would continue.
RHS director general Sue Biggs would not comment on Chatsworth directly but said: "In the Midlands and northern England we have very little apart from Tatton Park, so we're looking at things, whether it be a garden or a show.
"We will be at Tatton Park next year. If it remains successful it will still be there. We review our shows every year. We can't give any of our four gardens away but shows are a different thing."
She said that part of the reason for stopping working at Gardeners' World Live was because the RHS plans a garden in the West Midlands area.
An RHS representative said an announcement about a Chatsworth show will be made on Thursday.
Discussions are believed to have intensified after Dan Pearson worked with Chatsworth on Chelsea Flower Show 2015's best in show garden.
Biggs added that director of shows, retail and gardens David Morley who is leaving will have a like-for-like replacement.
Nick Mattingley is head of shows and David Edwards is new operations manager, but they are not in the RHS leadership team, as Morley's replacement will be. Biggs said the RHS has the "strongest shows team we've ever had now".
She added: "David was honest enough to say as a retailer he enjoyed doing the detail but the breadth was not for him. He has done great work merchandising for us on the retail side."