She is set to interview at Florida in the coming days, according to the report.
Hammon became the first full-time, paid female assistant on an NBA coaching staff when she was hired by the Spurs in 2014. Many have believed she might one day become the first female head coach in the NBA.
"If anybody's going to do it, it would be her," Spurs forward David Lee told reporters on Tuesday.
However, Lee, a former Gator, also said he had offered his assistance to her if she had any questions about Florida.
"Knowing the makeup of the campus and how the women's basketball is there, she'd be a great fit," he said.
Spurs coach Gregg Popovich said Hammon has been "an integral part of what we do and been a fantastic coach for us."
Hammon joined the Spurs staff immediately after she retired from the WNBA, where she had a 16-year career as one of the league's greatest point guards, despite having been undrafted out of Colorado State.
The Associated Press contributed to this report.