"At this point, I think it's obvious that something has to change around the governance," Nadella said.
He added that Microsoft would have "a good dialogue with their board on that", but he didn’t say if his outfit would want a seat at the table.
OpenAI's board consists mainly of outsiders and needs to be tasked with maximising shareholder value.
No board members have shares in OpenAI, and their mission is to “create 'broadly beneficial' artificial general intelligence, or AGI."
Nadella dismissed concerns of long-term damage at OpenAI and said the critical artificial intelligence research continues, as does the partnership with Microsoft.
But his comments didn't clarify where Altman and fellow OpenAI co-founder Greg Brockman, the company's chairman, will ultimately end up.
Early Monday morning, Nadella said that Altman, Brockman, and their colleagues would join Microsoft as part of a new AI research group.
That post followed news that ex-Twitch CEO Emmett Shear had been named OpenAI interim head as Altman looked to depart.
Hundreds of OpenAI employees signed a letter to the company's board demanding that they resign, or the staffers may choose to leave and join their former boss at Microsoft.
Nadella said it's the choice of OpenAI employees whether they stay in their current roles or move to Microsoft, adding that his company has what it needs to keep innovating on its own.
"I'm open to both options," he said.
Nadella said Vole respects OpenAI's nonprofit roots and believes AI must be developed and rolled out safely.
"We want to make sure that we're dealing with not only the benefits of technology but the unintended consequences of the technology from day one, as opposed to waiting for things to happen," Nadella said.