The midfielder was one of 11 senior players at Ibrox to be released after the club failed to win promotion to the SPFL Premiership.
Black, not always a popular figure among Rangers supporters, was a regular fixture in the side during his first two seasons at the club.
In total, the former Hearts midfielder, 30, made 99 appearances for Rangers and scored a total of eight goals.
He said: “Touch wood, I’ve been injury-free and I’ve not had any operations or bad injuries so that’s a benefit.
“I’ve got a few options down south and I think I’m going to go there. It’s just a case of weighing them up, picking one and hitting the ground running with the challenge.”
Black is the latest freed Rangers player to voice his displeasure at the acrimonious way they left the club.
Kris Boyd, Jon Daly and Richard Foster have all reacted negatively to criticism, with the latter claiming on Wednesday nobody had officially told the group they were no longer required.
Black added: “We had to read in the papers we had all been released, which was obviously disappointing.
“The boys that were there achieved two promotions then had a bad season last season but to not get a thank you or a phone call just to say thanks… You’d probably respect that more. None of us have received it.”