Dayton, Ohio-based Reynolds, which provides business management software for auto dealers in North America and Europe, had hired technology-focused investment bank Qatalyst Partners to run a sale, people familiar with the matter told Reuters in October.

The process has progressed and is now in its final stages, though no decision is expected before January, the sources said.

Reynolds may be sold to Carlyle or KKR for between $4 billion and $5 billion, less than the company had hoped, one of the people added.

The people spoke on condition of anonymity because the negotiations are confidential. Spokesmen for Reynolds, Carlyle and KKR declined to comment.

Reynolds sells software tools that allow car dealers to run their operations, including providing car dealer websites, digital advertising and marketing services, as well as data archiving.

Reynolds was founded in 1866 by Lucius Reynolds and his brother-in-law as a company that prints standardized business forms. It started to serve automotive retailers as major clients in the 1920s.

In October 2006, the company was acquired by Universal Computer Systems (UCS) for $2.8 billion. The merged company retained the Reynolds name and is currently headed by Chairman and Chief Executive Bob Brockman, who used to run UCS.

Brockman's $2.8 billion buyout was funded primarily by a group of investors that included Goldman Sachs Capital Partners, the private equity arm of Goldman Sachs Group Inc, and Vista Equity Partners.

(Reporting by Greg Roumeliotis and Soyoung Kim in New York; editing by John Wallace)

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