International Business Machines
The source, who was not authorized to speak publicly about the deal, said a final price was not set, but IBM may pay Sun around $9 to $10 per share.
The Wall Street Journal earlier reported IBM reduced its offer to $9 to $10 per share from a previous $10-to-$11 range.
IBM and Sun officials declined to comment.
A takeover of Sun would give IBM a clear lead in the $45 billion server market against Hewlett-Packard Co
A deal would have the most impact on IBM's high-end server business, giving it 65 percent of a market worth some $17 billion, versus 27 percent for HP. It would also bolster IBM's highly profitable software business and help ensure the survival of much-smaller Sun.
But some analysts say Sun's lackluster performance could hurt IBM. Sun rose to prominence in the 1990s, but never fully recovered after the dot-com bubble burst earlier this decade, and failed to make much profit from software products like Java and Solaris.
Some analysts also say the deal could spark antitrust scrutiny as customers and suppliers raise concerns about competition.