The best outcome for Microsoft would be to use this moment to double-down on its own homegrown AI initiatives, while making sure it can still benefit from — but not depend on — OpenAI's technologies.

Bret Taylor, the chairman of OpenAI’s board, said the artificial intelligence company was “not for sale.” Mr. Musk is separately raising money for his A.I. start-up, xAI.

OpenAI attorney William Savitt in a letter to Musk's attorney Friday said the proposal “is not in the best interests of OAI’s mission and is rejected.”