NEW YORK, Feb 12 (Reuters) - National Amusements Inc's negotiations with lenders to restructure debt have made "substantial progress" and a deal should be reached shortly, Chairman Sumner Redstone said on Thursday.

The company, which owns controlling stakes in CBS Corp (CBS.N: Quote, Profile, Research) and Viacom Inc (VIAb.N: Quote, Profile, Research), has been in talks for months about refinancing $800 million in debt that was due at the end of the year. It has a total of about $1.6 billion in debt outstanding.

"Constructive dialogue is continuing and I must tell you there has been very substantial progress since I last spoke to you," Redstone said on a conference call to discuss Viacom's quarterly earnings. "Indeed, I have been advised that an agreement acceptable to all parties is now within reach."

National Amusements sold about $230 million of shares of CBS and Viacom last fall to help meet debt payments, but Redstone said on Thursday that there had been no additional sales and none were expected.

"Since that sale, I can confirm that National has not sold and does not expect to be required by its lenders to sell any additional shares of CBS and Viacom. Not a share," he said. (Reporting by Paul Thomasch; Editing by Derek Caney)