SAO PAULO, Sept 1 (Reuters) - JPMorgan Chase & Co has reached an agreement with Brazil's Banco Bradesco SA to potentially transfer its private banking clients to the Brazilian lender, according to a document filed by Bradesco.

JPMorgan has roughly 20 billion reais ($3.71 billion) under management in its Brazilian private banking unit, a source said.

Bradesco also said that JPMorgan will continue to provide Brazilian clients with products and services abroad.

Under the terms of the agreement, clients may opt to migrate to the Brazilian bank. "Bradesco will act to enable an organized transition for the benefit of the clients," Brazil's second largest private-sector lender said.

JPMorgan did not immediately respond to a Reuters request for comments on the matter.

($1 = 5.3871 reais) (Reporting by Carolina Mandl )