Both stars could become free-agents next season if they opt out of their current deals. A host of other players, including Dwyane Wade, Amar'e Stoudemire and Chris Bosh have early-termination options on five-year deals signed in the summer of 2010.
Luol Deng, Danny Granger, Andrew Bogut and Dirk Nowitzki will all be unrestricted free agents next summer. The team also has to decide what to do with Kobe Bryant, who is entering the final year of his contract this season.
James, a two-time NBA Finals MVP, said recently that he isn't thinking about the summer of 2014.
Lakers lost out on center Dwight Howard when he decided to sign with the Houston Rockets instead of signing a five-year deal with the team.
More from ESPN.com:
Opinions are split on whether the Lakers can actually land James or Anthony, with one source calling it "realistic" and another saying it was "far-fetched at this point." Nonetheless, the Lakers have made it clear they are positioning themselves for a run at one and perhaps even two of the superstars who could become free agents in 2014 by refusing to commit to any contract past this upcoming season, multiple sources have said.