The 38-year-old was released by boss Mark Yates at the end of last season after scoring 11 goals in 23 League Two starts.
But having been training with the Robins while looking for a move elsewhere, he now looks set for a surprise return.
Cureton played 45 minutes of Cheltenham's friendly draw with Evesham United and Yates explained that they have opened discussions.
"Jamie came down and trained with us, looking fit, strong and as good as ever," Yates told the Western Daily Press.
"It's become an option and we have been talking. I have no problems with Jamie or what he did for us last season, so we will see.
"I think he will be good to have around for our other forward players."