Sources said the Cavaliers and Varejao -- one of LeBron James' most beloved teammates -- are closing in on a new three-year deal worth an estimated $30 million that would kick in starting with the 2015-16 season.
Varejao has spent his entire NBA career with the Cavaliers after Cleveland acquired his rights on draft night in 2004.
The Cavaliers and Varejao, sources said, have been eager to finalize terms on a new pact before the start of the new season. Cleveland opens its campaign Thursday by hosting the New York Knicks.
Varejao, 32, was in the final year of a six-year, $49 million pact and is earning $9.7 million this season. The Brazilian started for the Cavaliers in Thursday's opener against the Knicks ahead of the younger Tristan Thompson, who is also hoping to secure a contract extension before Friday's deadline for first-round picks from the 2011 draft to receive extensions from the teams that drafted them.
Varejao appeared in 65 games last season, averaging 8.4 points and 9.7 rebounds in 27.7 minutes per game.