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Davis will meet with his agent, Rich Paul, in the coming weeks to come up with a multi-year contract term best-suited for the 27-year-old megastar, per the report.
Davis averaged 26.1 points in his first year with the Lakers, which ended last week with another NBA title for the franchise but the first for the eight-year player out of Kentucky.
Davis is averaging 24.0 points and 10.4 rebounds and 2.4 blocks per game for his career.
Davis and the Lakers have been installed as early favourites to repeat as NBA champions in 2021.