The two sides spoke Saturday and were closing in on a two-year deal worth roughly $11 million, according to a person familiar with the negotiations who spoke on condition of anonymity because the deal hasn't been finalized.
Greene reportedly was going to ask for $4.9 million in arbitration, while the club was expected to offer $4 million.
The soft-spoken Greene was named the team's 2007 MVP after hitting .254 and setting career highs with 27 homers, 44 doubles and 97 RBIs. He also played in a career-best 153 games after missing time in previous seasons due to injuries.
Greene set a club record with a .984 fielding percentage over 690 chances.
Retaining Greene is important since he's one of the Padres' few homegrown talents. He was the 13th pick overall in the 2002 draft and made his big-league debut on Sept. 3, 2003.
In December, the Padres gave another homegrown player, NL Cy Young Award winner Jake Peavy, a $52 million, three-year contract extension. It is the biggest deal in club history.