The deal comes as both companies' corporate clients seek more bandwidth and faster capabilities to move data to run their businesses. It would combine Level 3's enterprise services with CenturyLink's network that provides Internet and telephone offerings to millions of customers.
The market for corporate customers' voice and data services has been estimated by analysts to be worth anywhere from $57 billion to $100 billion in revenue per year.
The deal could be announced as soon as next week, according to one of the people.
CenturyLink and Level 3 declined to comment. The Wall Street Journal first reported the news earlier Thursday.
The people asked not to be named because the talks are private.
A merger with CenturyLink would be the latest evolution for Level 3, a Colorado-based company which narrowly avoided bankruptcy in the early 2000s and made an $5.65 billion acquisition last week of tw telecom Inc in 2014.
Level 3 struggled during the downturn but got a cash infusion of $500 million in 2002 from investors including Warren Buffett.
In the decade that followed, Level 3 consolidated at a rapid clip and picked off the remains of the most desirable U.S. fibre networks, including Global Crossing.
Singapore's Temasek is a large shareholder in Level 3. CenturyLink is based in Louisiana.
(Reporting by Liana B. Baker and Greg Roumeliotis in New York; Editing by Bernard Orr)
By Liana B. Baker and Greg Roumeliotis