The proposed cap would restrict CMC feeds to 15-30%, depending on how much redress a consumer is due.
The maximum charge under the proposals falls into five redress bands, with the maximum percentage falling the higher the consumer redress obtained.
The cap will apply to all claims where a consumer is awarded monetary redress other than PPI claims which are already subject to a 20% cap set by Parliament.
Some consumers currently pay fees of more than 40% of their compensation, according to the regulator.
Under the proposals CMCs will also be required to disclose key information, including giving consumers more information about how the fees they pay will be calculated and better signposting to the free alternative routes to redress available. This information must be disclosed to consumers before they enter into a contract.
The consultation is open until 21 April 2021 with a policy statement expected to be published this autumn.
The majority of claims currently being managed by CMCs relate to packaged bank accounts, loans, savings and investments, and pensions.
Sheldon Mills, executive director of consumers and competition at the FCA, said: “We took over regulation of CMCs in April 2019, and have since been proactively supervising the sector. When working well, CMCs can provide useful services for consumers. However, consumers can experience harm when they do not understand the nature of the service CMCs provide and where they are charged excessive fees. The proposals we have announced today are designed to address this.”