The deal will reportedly be worth an estimated $30 million and would begin with the 2015-16 season.
Last week, Cavaliers coach David Blatt announced that Varejao will start at center in Cleveland's opener versus the New York Knicks on Thursday. According to Stein, the team has been "eager" to finalize a deal with the 32-year-old before the start of the season.
Varejao averaged 8.4 points, 9.7 rebounds and 2.2 assists in 65 games last season. He has spent his entire career with the Cavs after being traded to Cleveland by the Orlando Magic shortly after being drafted in 2004.
The veteran was averaging career highs of 14.1 points and 14.4 rebounds through 25 games in 2012-13, but was hospitalized for a blood clot in his lung in January 2013 and missed the rest of the season.
- Molly Geary