Anthony, who averaged 27.4 points and 8.1 rebounds last season with the New York Knicks, can make more money if he re-sign with the Knicks, but has stated his desire to win a championship.
The Lakers, who missed the playoffs for only the sixth time in the franchise's history last season, are currently the only NBA team without a head coach after the Brooklyn Nets hired Lionel Hollins.
Clearly, the Lakers feel as though they are not in rebuilding mode, but only have three players under contract for next season: Bryant, who will make $23.5 million, point guard Steve Nash ($9,701,000) and center Robert Sacre ($915,243).
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Anthony is far from a consolation prize, however. Sources indicate the Lakers are enamored with his game and believe he would complement Bryant well. The Lakers hope to pair the two wings with center Pau Gasol, whom they met with on the first day of free agency.
ESPN reported Wednesday night that the Oklahoma City Thunder duo of Kevin Durant and Russell Westbrook made a strong case to the Spaniard, with the Thunder emerging as a surprising front-runner, despite their financial limitations. The Chicago Bulls are scheduled to meet with Gasol on Thursday in Los Angeles.