The option is worth close to $2.2 million next season, and Williams has made his intentions clear to the Cavaliers, the report said.
Williams, 33, was signed to a two-year, $4.3 million contract last summer by the Cavs to give them depth after star guard Kyrie Irving was injured in the 2015 NBA Finals.
Williams made 14 starts at the beginning of the season while Irving recovered from offseason knee surgery. He averaged 8.2 points and 2.4 assists in 41 games in the regular season.
Williams was bothered by soreness in his knee for much of the season and was diagnosed earlier in the season with chondromalacia, or an irritation of the cartilage under the kneecap, which resulted in him receiving a platelet-rich plasma injection in the knee.