Murphy made his comments to FoxSportsWisconsin.com during the Packers' Tailgate Tour.
"We want to have [Favre] back in the family," Murphy told the website.
Murphy said last year that the team hoped to retire Favre's No. 4 jersey at some point. Murphy said Tuesday, "it's got to be the right time for him and us" for that ceremony to happen.
"I thought he and Aaron jointly presenting the Comeback Player of the Year Award was a great first step," Murphy told FoxSportsWisconsin.com.
The awkward handshake between Favre and Rodgers signaled a mending of sorts in the relationship between Favre and the Packers that had been frayed since 2008, when the Packers traded Favre to the New York Jets after he came out of retirement, choosing to go with Rodgers as their quarterback. Favre signed with the Minnesota Vikings, the Packers' NFC North archrival, a season later, further weakening the bond between the star quarterback and the team.
Favre told ESPN's Mike Tirico in his "Monday Night Football" podcast last September that he had begun to get over any hard feelings he held toward the organization, with which he won three MVP awards and a Super Bowl title.
"We don't need to shake hands and move on," Favre said. "I think in some ways that has happened. … Even though it's a shame the way things went down between I and the Packers, as time goes by, it's like a grudge … you just kind of get over it, you know?"
Information from ESPN.com NFC North blogger Kevin Seifert was used in this report.