Trust could run Merthyr Tydfil's Cyfarthfa Park and Castle
A not-for-profit trust could take over responsibility for some of Merthyr Tydfil's council-run services in a bid to save £330,000 a year.
Cyfarthfa Park and Castle as well as libraries and leisure centres could be handed over to the new organisation.
Merthyr Tydfil council said the trust would be able to access additional funding and could deliver financial savings.
A public consultation has been launched and it is open until 23 June.
The council has organised drop-in sessions at Merthyr Tydfil Leisure Centre on 10 June and Treharris Community Centre a day later, between 16:00 and 20:00 BST, to discuss plans for Merthyr Tydfil Leisure and Culture Trust.
The authority said the proposals were part of phase two of its efficiency programme.
Cyfarthfa Park and the Cyfarthfa Castle Museum and Art Gallery is a popular tourist destination. It was the home of ironmaster Richard Crawshay and was built in 1824.
The castle museum reopened in 2011 after a £320,000 restoration.
Other councils around Wales are also looking at alternative ways of running leisure services in the face of budget cuts.