French upstart telecommunications company Iliad SA has made an offer for T-Mobile US Inc., in a bold bid to counter an offer for the country's fourth-largest wireless carrier by Sprint Corp., said people familiar with the matter.

The contours of the offer, which was made less than a week ago to T-Mobile's board, are unclear, but one of the people said it involves control of the U.S. company. It's unclear what, if any, the response to the bid has been.

T-Mobile US had a market value of $24.8 billion. Iliad's was EUR12 billion ($16 billion) and it's not clear how the French company would pay for such a deal. Iliad is working with several banks to secure financing, one of the people said.

Iliad, which has sparked a fierce price war in France's mobile-telephone market via its cut-throat rates, sees the offer as a "one-time opportunity to enter the world's-largest telecoms market," said the person.

Sprint and T-Mobile US have been pursuing a combination for months, and the two sides have agreed on the broad outlines of a deal valuing T-Mobile US at more than $30 billion, people familiar with the matter have said. Any announced deal between Sprint, which is majority-owned by SoftBank Corp., is expected to face stiff antitrust scrutiny.

Iliad believes its offer for T-Mobile US, which is owned by Deutsche Telekom AG, would be favorably viewed by U.S. regulatory authorities because the company is not active in the U.S., the person said.

Ryan Knutson and Tom Gryta contributed to this article.