Gaxa, who played six league games last term for the champions, was seemingly part of coach Gavin Hunt's plans as he attended a pre-season camp in Cape Town.
However, the ex-Kaizer Chiefs and Mamelodi Sundowns fullback was notably absent from the squad that Wits registered with the PSL for 2017/18.
Gaxa had a one-year option on the deal he penned with the Students following his release from Chiefs, but it was not exercised.
The experienced 33-year-old is currently on the search for a new club.
"He's not registered with Wits because we haven't sign a contract," Binkin tells KickOff.com.
"We are looking at that [other clubs] as an option," he adds.