The 49ers later confirmed that Lee had signed a six-year contract extension.
"The 49ers are pleased to have reached a long term contract extension with Andy," general manager Trent Baalke said in an announcement from the team. "Andy has established himself as one of the top players in the game at his position. He is a valued member of our organization and community. As we stated earlier this year, it is our objective to keep the core of this team together long term, and this is just another step in that direction."
San Francisco CEO Jed York hinted at an extension for one of the team's All-Pro players earlier on Wednesday.
"Which @49ers all-pro will get an extension next? 1st person to respond correctly will get a football with his autograph," York wrote.
Lee was scheduled to earn $1.1 million in 2012, the final year of a six-year, $7.115 million contract he signed after the 2006 season. Financial terms of his extension weren't immediately known, but Maiocco said the deal is expected to be in the $4 million per year range, which would pull Lee even in average per year with Oakland Raiders kicker Sebastian Janikowski and punter Shane Lechler, the highest-paid specialists in the NFL.
A source told Maiocco later Wednesday that Lee is set to make $20.5 million over the course of the extension, including $7.1 million over the first two seasons.
A sixth-round pick out of Pittsburgh by the 49ers in 2004, Lee has a net average of 39.0 yards per punt over his 128-game career, with 209 of 723 punts placed inside the opponents' 20-yard line. In 2011, Lee led the NFL with a 50.9-yard gross average and set an NFL single-season record with a 44.0-yard net average earning a third trip to the Pro Bowl and the third All-Pro nod of his eight-year career.