Lopez just completed his seventh season with the Nets since being selected in the first round of the 2008 draft. The 27-year-old signed a four-year, $60 million max deal in July 2012.
According to Adrian Wojnarowski of Yahoo! Sports, Brooklyn remains a "strong frontrunner" to re-sign Lopez.
Over 72 games last season, Lopez averaged 17.2 points and 7.4 rebounds while shooting 51.3 percent from the field. On Thursday Brooklyn traded power forward Mason Plumlee to the Portland Trail Blazers.
Last season the Nets went 38-44 and earned the No. 8 seed in the Eastern Conference before falling in the first round of the playoffs.