Williams, who is suspended indefinitely for his admitted role in overseeing a bounty system that offered Saints defenders cash for big hits, did not immediately respond to a phone message and email left with his foundation in Missouri on Thursday.
Pamphilon made the recording during a meeting before the Saints lost to the 49ers in a divisional playoff game in January.
When the New York Giants defeated the 49ers a week later in the NFC title game, several Giants players made similar comments about wanting to get hits on Williams, who fumbled twice in the game, because they knew he had previous concussions.
In Pamphilon's recording, Williams also tells his players to set their sights on running back Frank Gore, receiver Michael Crabtree and quarterback Alex Smith.
"We need to decide on how many times we can beat Frank Gore's head," he says.