An official within the league who is very close to the Nets' management team said the team would also consider going after Utah Jazz forward Carlos Boozer if James rejected the offer that was presented by new owner Mikhail Prokhorov and a team that included hip-hop mogul Jay-Z.
Nets president and general manager Rod Thorn said in a text message on Tuesday that there was nothing to report on the free agency front.
James is planning to announce the team with which he will sign during a one-hour special on ESPN Thursday night, ESPN The Magazine's Chris Broussard has learned through independent sources.
It's the same message the 69-year-old outgoing executive has given out for past five days as the Nets and the rest of the NBA waits for the two-time MVP to decide whether to remain with the Cleveland Cavaliers or to accept one of the offers from the Nets, Knicks, Clippers, Heat or Bulls.
James has given no indication when he will make a decision. He visited his summer camp in Akron, Ohio, on Tuesday and, appropriately, kept everyone waiting four hours for his arrival.
Asked about the Nets' options if The King nixes their overtures, Thorn wrote:
"We will look at other options if we don't get one of the top guys."
That leaves Boozer and Lee for the Nets to go after if the top three reject the offer to come to New Jersey and play for a team that won a league-worst 12 games last season.
Mark Bartelstein, who represents Lee said the lines of communication have been open between him and Thorn about Lee, who averaged 20.2 points and 11.7 rebounds this past season.
"We've talked a bunch," Bartelstein said in a telephone interview. "There is not a day that goes by that we don't talk. They are kind of waiting now on Wade and LeBron and once they decide, we'll go from there."
Bartelstein said there are a lot of other teams actively pursuing Lee and there is a chance that he might be signed before James makes a decision.
"If he is available when the Nets know where they stand with LeBron, we'll be happy to talk to them," Bartelstein said. "They've got a lot of great things going on in the organization and, you know, David loves New York and the area, but I don't know if David will still be there when they have an answer."
Rob Pelinka, Boozer's agent, did not respond to an e-mail seeking comment on his client.
The Nets official who requested anonymity said the team would not overspend this year just to sign someone, noting they would rather wait until next year.
In the past two days, two men mentioned as possible successors to Thorn as the Nets general manager both said they were happy where they were. Joe Dumars of the Detroit Pistons and Jeff Bowers of the New Orleans Hornets issued statements saying they would not be coming to New Jersey.
Information from The Associated Press was used in this report.