Private equity firms Welsh, Carson, Anderson & Stowe and Hyde Park Holdings LLC are selling the U.S. logistics company. The rise of e-commerce has increased companies' demand for shipping, making logistics companies more valuable. Private equity firms have recently been cashing in on that trend.

The price in this deal represents a multiple of about 10 times Ozburn-Hessey Logistics' $80 million of annual earnings, the people said.

The deal is slated to be announced in the coming weeks according to a person familiar with the matter. The people asked not to be named because the deliberations were private.

Geodis and Ozburn-Hessey Logistics did not immediately respond to requests for comment. Neither of the New York-based private equity firms responded to requests for comment.

Founded in 1951 and based in Brentwood, Tennessee, Ozburn-Hessey Logistics has more than 120 distribution centres. It has customers in the apparel, electronics, healthcare, food and beverage, and consumer packaged goods industries. Clients include Starbucks Corp (>> Starbucks Corporation), Apple Inc (>> Apple Inc.), Red Bull and General Motors Co (>> General Motors Company).

In April, France's Norbert Dentressangle SA (>> NORBERT DENTRESS.) agreed to sell itself to Stamford Connecticut-based XPO Logistics Inc (>> XPO Logistics Inc) in a deal valued at $3.53 billion, including debt, making XPO one of the top 10 logistics companies in the world.

Also in April, FedEx Corp (>> FedEx Corporation) announced a deal to buy Dutch delivery service company TNT Express (>> TNT EXPRESS) for 4.4 billion euro ($4.9 billion).

FedEx's main rival, package delivery company, United Parcel Service Inc (>> United Parcel Service, Inc.) agreed to pay $1.8 billion for Chicago-based Coyote Logistics from private equity firm Warburg Pincus to expand its full-truckload services in July.

(Reporting by Mike Stone in New York and Pamela Barbaglia in London; Additional reporting by Greg Roumeliotis in New York; Editing by Bernard Orr)

By Mike Stone and Pamela Barbaglia