The 32-year-old only made eight Premier League starts over the course of his second spell at his boyhood club as the injuries problems that have plagued much of his career continued.
“He’s out of contract. I had a conversation with Andy,” Bruce said after Sunday’s preseason friendly against York City.
“I think he wants to go and play. I wish the lad all the best. I hope it goes for the rest of his career.
“He’s certainly been a big help to me in the last couple of years, that’s for sure.”
Carroll left Newcastle in January 2011 to join Liverpool in a £35m transfer, but he only scored 11 goals in 18 months at Anfield before he left for West Ham, initially on loan and then for a £15m permanent transfer.