The deal, which is still pending a physical, could be officially announced on Sunday. It reportedly includes a no-trade clause.
Giants chief executive Larry Baer and Pence spoke at Pence's locker after Friday night's game while reporters were present. Baer said he only congratulated Pence for winning the team's Willie Mac Award, given to the team's most inspirational player. However, Pence said the two sides were set to discuss a contract extension before free agency starts.
Pence helped the Giants win the World Series last year after they acquired him from the Philadelphia Phillies late in the season.
Pence was seeking a five-year deal worth at least $85 million, similar to the deal the Dodgers gave to outfielder Andre Ethier.
Early, the Giants reportedly suggested an offer similar to the one Cleveland Indians outfielder Nick Swisher got: four years for $56 million.
General manager Brian Sabean has said re-signing Pence is the team's biggest priority this offseason. The Giants also hope to hang on to pitchers Tim Lincecum and Javier Lopez.
Pence, 30, has 26 home runs and 94 runs batted in, and started each of the first 160 games this year.
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The New York Mets agreed to a two-year contract extension with manager Terry Collins, CBSSports.com reported.
ESPNNewYork.com reported earlier that the deal includes a team option for 2016.
An official announcement is likely on Monday.
Collins, 64, is 224-260 in three seasons as the Mets' manager going into Saturday's game against the Milwaukee Brewers.
The Mets are in third place in the National League East at 73-87 with two games left this season.
The team is dealing with the season-ending losses of right-handed ace Matt Harvey to a ligament tear and closer Bobby Parnell to a herniated disk. All-Star third baseman and captain David Wright recently returned after spending nearly two months on the disabled list because of a hamstring injury.
New York also traded away outfielder Marlon Byrd and catcher John Buck to the Pittsburgh Pirates.
Before coming to New York, Collins managed the Houston Astros (1994-96) and Anaheim Angels (1997-99). He also managed in Japan.
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Former Detroit Tigers outfielder Gates Brown has died, the team announced. He was 74.
Brown spent his entire 13-year career with the Tigers. He was part of World Series championships in 1968 as a player and 1984 as a coach.
He hit .370 in 67 games with the Tigers in 1968. For his career, he batted .257 with 84 home runs.