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The deal, which was reported by NBC Sports, comes after Odom had a difficult few months at the Dallas Mavericks. He left the team in April.
A source has reportedly confirmed the rumours to E! Online but said that the deal has not yet been finalised.
The insider also claimed that Odom's wife Khloe Kardashian is "thrilled" at the possibility that her husband will be playing in Los Angeles.
The couple announced in April that they had decided to put their reality show on hold, reportedly so that Odom could concentrate on his basketball career.
Rumours have also suggested that the pair are keen to start a family.
