While it may get ratings for their show this kind of rumor would pretty much end his NBA career. Yes he was not getting the offers he wanted (dunno why he seems to only want the Lakers) but after this I doubt he gets one from any team.
Odom's had a serious love-hate relationship with the Lakers.
He never wanted to leave there for the longest time, threatening to retire rather than go to Philly for Andre Iguodala.
When the aborted CP3 deal was announced, sending him to New Orleans, he fricking lost it and pouted his way out to LA under the "If they don't want me here, I don't want to be here!" logic.
I think he realized what a colossal frickup that was once he got sent to Dallas, to the point where Mark Cuban got sick of his shite and sent him home before the end of the regular season.