ESPN.com's Tim MacMahon and Marc Stein reported the news.
Williams, 32, played his first five-plus seasons in Utah before being traded to the then-New Jersey Nets in 2011. He made two of his three All-Star teams and both of his All-NBA teams in a Jazz uniform.
In his second season in Dallas, Williams is averaging 13.1 points and 6.9 assists per game at the All-Star break. He will become an unrestricted free agent this summer.
A Williams-Jazz reunion would rank among the unlikeliest in recent NBA memory. Utah moved on from Williams amid years of internal discord, including a sour relationship with former coach Jerry Sloan that led to the Jazz legend's resignation. The team traded Williams, then their franchise star, within weeks of Sloan's resignation.
Utah fans understandably held a grudge for years, continuing to boo every time a Williams-helmed team arrived in Salt Lake City. Their disdain for Williams has not even subsided despite the Jazz building a playoff-worthy roster, somewhat on the backs of players acquired in the Nets trade.
That said, there has been some thawing of relationships behind the scenes. Sloan, now a special adviser to the organization, and Williams met last season to bury the hatchet. Williams also maintains an offseason home in Utah.
"I had great years here, some of the best years of my career," Williams said, per Eddie Sefko of the Dallas Morning News. "This place is still special to me. I still make it my home in the summer, so I love coming back here and loved my time with the Jazz."
Williams would have to approve any trade because he would relinquish his accrued Bird rights with the Mavericks.
The Jazz's motivation largely stems from starting point guard George Hill's injury issues. Hill has dealt with a sprained toe for most of the first half of the season, missing 25 games. While he has been a revelation when in the lineup, Hill's absence has exposed the weaknesses in Dante Exum and Shelvin Mack's ability to run an offense.
With Utah hanging around as a potential No. 4 seed in the West, adding Williams could provide a short-term insurance policy for the second half.