Though NFL Commissioner Roger Goodell continues to have the solid support of many of the league’s 32 owners, the group is prepared to act against Goodell, potentially considering his dismissal, if the investigation by former FBI director Robert S. Mueller III concludes that Goodell was guilty of willful and egregious misconduct in the handling of the Ray Rice case, several people familiar with owners’ views said Thursday.

“He’s been a very good commissioner and he’s done great things for the league,” a high-ranking executive with one NFL team said. “The presumption is that he’s telling the truth and the investigation will demonstrate that. We’ll go by the report [generated by Mueller’s investigation]. If the report says something different, we’ll take the appropriate action.”

That executive and others spoke on the condition of anonymity, citing the investigation.

An official with another NFL team who had been briefed on the views of the owner of his franchise said of that owner: “He supports the commissioner.” Asked what it would take for that owner’s support of Goodell to be withdrawn, the official said: “If the investigation concludes that the commissioner saw more and knew more than he has said, and he was not truthful about that to the clubs, things would change.”

A top executive with a third franchise who had spoken to his team’s owner expressed similar sentiments, saying Goodell’s job would be at risk only if it is found that he personally orchestrated a cover-up.

“Certainly he would be [held] accountable for intentionally misleading people and taking actions to cover his tracks,” that executive said. “Certainly that would be grounds for anything from a reprimand to termination. [But] it would take a lot. No one expects it to come to that.”

According to that executive, owners would have little choice but to consider firing Goodell if Mueller’s report concludes that Goodell acted improperly in a significant way.

“The integrity of the league would have to be protected at a certain point,” the executive said, relating what he called the thoughts of that team’s owner. “The trust of the public would have to be maintained. But, again, that’s not the expectation here.”

Goodell is thought to have the strong support, several people within the league said, of a group of powerful and influential owners that includes the New England Patriots’ Robert Kraft and the New York Giants’ John Mara. Kraft defended Goodell during an appearance on CBS earlier this week. Mara issued a written statement Wednesday saying it was “misguided” to think Goodell’s job was in jeopardy.

Later Wednesday, the league announced that Mara and Art Rooney II, the president of the Pittsburgh Steelers, would oversee the investigation conducted by Mueller, now a Washington-based partner in the law firm WilmerHale.

The league’s announcement of the investigation came hours after the Associated Press quoted an anonymous law enforcement official as saying he’d sent a video of the Rice incident to the NFL months ago. The AP reported that the official provided a voice mail from a female with a phone number in the NFL’s offices acknowledging receiving the video in April.

The video, released publicly Monday by TMZ, shows Rice striking Janay Palmer, then his fiancée and now his wife, inside a hotel elevator in Atlantic City in February. Goodell and the league have said they did not see that video until Monday. They have said the NFL’s efforts to obtain the video from law enforcement were rebuffed.

Goodell made those points in a memo to NFL teams this week. An executive with one team said Thursday it would be “a problem” if Goodell is found to have lied in that memo.

Several executives with NFL teams expressed the view Thursday that the media and others are focusing wrongly on the potential missteps by Goodell rather than on the misconduct of Rice.

The Baltimore Ravens released Rice on Monday and the NFL suspended him indefinitely. The league initially suspended Rice for two games, a penalty which Goodell later called a mistake.

Despite calls for him to step down by the National Organization for Women and others, Goodell has remained adamant that he did nothing untoward and that he will not resign, according to people familiar with his thinking. One of those people said Wednesday night, following the AP report, that Goodell “never” will resign and there’s “no reason to.” Goodell told CBS this week he did not believe his job was on the line.