The deal, first reported by Sky News, is expected to be announced on Monday alongside news the joint venture will also close its loss-making megastores business in Britain.
The person said Carphone Warehouse would return some of the proceeds from the sale of a share in profits of Best Buy Mobile to its shareholders.
Carphone Warehouse declined to comment. Best Buy could not immediately be reached for comment.
(Reporting by Mark Potter; Editing by Matt Scuffham)