Gates owns about 4.5 percent of the $277 billion company and is its largest individual shareholder.
The three investors are concerned that Gates' presence on the board effectively blocks the adoption of new strategies and would limit the power of a new chief executive to make substantial changes. In particular, they point to Gates' role on the special committee searching for Ballmer's successor.
They are also worried that Gates - who spends most of his time on his philanthropic foundation - wields power out of proportion to his declining shareholding.
Gates, who owned 49 percent of Microsoft before it went public in 1986, sells about 80 million Microsoft shares a year under a pre-set plan, which if continued would leave him with no financial stake in the company by 2018.
(Read more: Cramer: Microsoft's dividend is a move of desperation)
Gates lowered his profile at Microsoft after he handed the CEO role to Ballmer in 2000, giving up his day-to-day work there in 2008 to focus on the $38 billion Bill & Melinda Gates Foundation.
In August, Ballmer said he would retire within 12 months, amid pressure from activist fund manager ValueAct Capital Management.
Microsoft is now looking for a new CEO, though its board has said Ballmer's strategy will go forward. He has focused on making devices, such as the Surface tablet and Xbox gaming console, and turning key software into services provided over the Internet. Some investors say that a new chief should not be bound by that strategy.
(Read more: Can Bill Gates save Microsoft?)
Microsoft is still one of the world's most valuable technology companies, making a net profit of $22 billion last fiscal year. But its core Windows computing operating system, and to a lesser extent the Office software suite, are under pressure from the decline in personal computers as smartphones and tablets grow more popular.
Shares of Microsoft have been essentially static for a decade, and the company has lost ground to Apple and Google in the move toward mobile computing.
One of the sources said Gates was one of the technology industry's greatest pioneers, but the investors felt he was more effective as chief executive than as chairman.