Murphy attended a meeting of the team's executive committee Friday. He was not available for comment afterward, but team spokesman Aaron Popkey said Murphy has "full confidence" in how Thompson and McCarthy are handling this matter.
Favre is having second thoughts about football after retiring in March. But the Packers have since committed to moving on without the three-time MVP, causing a public rift between the team and one of its greatest players.
Although the Packers are publicly owned, the seven-member executive committee meets in private and doesn't publicize its agenda. The meetings generally cover all aspects of the team's operation and typically include a football report. It was widely assumed, but not confirmed, that the Favre situation would be discussed Friday.
"Obviously, right now, this is going to be a heavy discussion," Davis said.
Favre's future also could come up during the Packers' annual shareholders meeting at Lambeau Field on July 24.
A movement to summon fan support for Favre has fizzled so far. A rally in Green Bay drew fewer than 200 fans Sunday, and Monday's rally in the Milwaukee suburbs drew only 30 despite widespread local media attention. But shareholders supporting Favre still could call attention to the issue.
Shareholders, who elect the team's board of directors but don't directly control the team's day-to-day decision making, aren't given the chance to ask questions during the meeting. But Murphy and Thompson will be there to mingle afterward.
The controversy comes at a difficult time for Murphy, whose father, Hugh, died Thursday in Florida at 83. Murphy returned to Green Bay for Friday's meeting, and planned to rejoin his family in Florida. A memorial is scheduled for Monday.
Murphy, a former All-Pro safety for the Washington Redskins, got his law degree from Georgetown and worked as an assistant executive director of the NFL Players Association after his playing days. He took over for longtime Packers top executive Bob Harlan in January. Before joining the Packers, Murphy was the athletic director at Northwestern.
Speaking on the Packers' statewide tour with fans last week, Murphy expressed support for Thompson and McCarthy regarding Favre.
Favre has flip-flopped before about his football future, but never like this. He teased the Packers earlier in the offseason and seemed set to unretire in late March, only to change his mind once again. His 11th-hour desire to unretire drew a decidedly lukewarm reception from the team this time.
Unless he is released or traded, Favre's rights belong to the Packers until his current contract expires after the 2010 season.
The Packers have filed tampering charges against the Vikings, believing that offensive coordinator Darrell Bevell, Favre's former quarterbacks coach in Green Bay, had contact with Favre that violated an NFL rule prohibiting teams from trying to "impermissibly induce a person to seek employment" while they are employed by another team.
A person familiar with the Packers' complaint told The Associated Press on Wednesday that Packers officials have expressed a belief that interest from the Vikings is the main reason Favre suddenly is considering a return to the NFL. The person requested anonymity because of the sensitivity of the situation.
On Wednesday, Favre's agent, Bus Cook, told ESPN that he and Favre have "no definite plans to ask for reinstatement" and it was up to the Packers to decide what to do next.