Marc Berman of the New York Post reported the update Tuesday.
Bullock signed with the Knicks as a free agent last July, but he didn't make his team debut until January because of surgery on a cervical disc herniation.
The 29-year-old UNC product struggled to make a consistent impact upon his return. He averaged 8.1 points, 2.3 rebounds and 1.4 assists while shooting just 40.2 percent from the field across 29 appearances (19 starts) before the season was indefinitely delayed because of the coronavirus pandemic.
His lackluster numbers didn't lead the coaching staff to look in a new direction, though.
"Interim coach Mike Miller fell in love with Bullock's basketball IQ, dogged defense and reliable 3-point shot," Berman wrote. "He was a mainstay in the rotation—even as fans/media begged for Miller to give more minutes to the young players such as Kevin Knox."
The Knicks have until June 28 to make a decision about whether to exercise the option, and he'll carry a $1 million dead-cap hit if the team declines it, per Spotrac.
In all, Bullock has averaged 6.9 points, 2.1 rebounds and 1.1 assists across 301 career regular-season games with the Knicks, Los Angeles Clippers, Phoenix Suns, Detroit Pistons and Los Angeles Lakers.
Although he's filled a key role this season, he could drop down the depth chart next year depending on the Knicks' offseason moves as they look to turn a corner in their extended rebuilding process.
Bullock would be better served as a sparkplug off the bench than a starter if New York has a serious eye on making the playoffs next year.