The incumbent Brooklyn Nets are then scheduled to meet with Williams on Monday evening to recap a pitch they've been making to their All-Star guard for weeks.
Williams will more than likely make his decision Tuesday, a source told ESPN The Magazine's Ric Bucher.
The Nets can offer Williams a five-year deal worth nearly $100 million. The Mavericks can only counter with a four-year deal in the $75 million range but will try to sell Williams on the appeal of not only playing for his hometown team but teaming with the proven championship combo of star forward Dirk Nowitzki and coach Rick Carlisle.
Sources close to the situation told ESPN.com that Nowitzki -- who has maintained a friendship with Williams over the past few seasons -- and Mavs owner Mark Cuban have been making their recruiting pitches to Williams by phone since free agency began Sunday at 12:01 a.m.
"@DeronWilliams Dallas fans are waiting on your arrival," he wrote.
With Nowitzki traveling abroad this week and Cuban in Los Angeles working on his "Shark Tank" television show, sources say that Dallas will be represented in Monday's sitdown with Williams by president of basketball operations Donnie Nelson, coach Rick Carlisle and former Mavericks franchise player Michael Finley, who is making the trip in an unofficial ambassadorial role.
In reality, though, Dallas' lead recruiter in the quest to sign Williams is Mavericks point guard Jason Kidd, who has spent the bulk of the week in close proximity to Williams in the Hamptons on a golf vacation.
ESPN The Magazine's Chris Broussard reported Sunday that Williams remains "torn" by the difficult decision, but the 28-year-old remains on course to choose his destination by Independence Day so he can report to Team USA training camp in Las Vegas on July 5.
The Nets' meeting with Williams will follow a morning sitdown with free agent point guard Steve Nash, according to sources close to the process.
The Nets have interest in Nash both as a prime replacement for Williams should they lose Williams to Dallas but also as a potential backcourt mate for Williams.