The report says Cousins could have a deal signed before the Kings open training camp next week and could be seeking a five-year max deal in the $80 million range that teams can award their designated franchise players.
Cousins, 23, is set to make $4,916,973 this season.
Cousins averaged 17.1 points and almost 10 rebounds for the Kings last season. The Kings have missed the playoffs in each of the past seven seasons.
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After announcing the addition of future Hall of Famer Shaquille O'Neal as a minority owner and mentor to Cousins, Ranadive told USA Today Sports: "I don't want to say anything premature [about an extension], but I've been constant in my support for DeMarcus. I reached out to him when we first closed the deal. He was the first person I reached out to. They're out there practicing on their own every day, and he's out there leading those practices. He's out there with the team practicing every single day by themselves. They all came to Sacramento early. I don't know if that's ever happened.