The Mavericks will get the first shot at Williams, as he is scheduled to be in Dallas on Monday morning before heading back to Brooklyn that evening, according to Marc Stein of ESPN.
Brooklyn can offer more money to Williams, but Dallas has the appeal of being Williams' hometown team. Dallas also has the more talented roster, but Brooklyn is looking to add Dwight Howard and Joe Johnson.
Williams has said he wants to have the situation resolved by July 5 so he can report to Team USA training camp.
His decision is also of great importance to Jason Kidd, who has said he will join Williams on whatever team he signs with.