The PM will make the mercy plea with the President of Indonesia Joko Widodo during his state visit to Indonesia, hoping to "help the family concerned".
"On the issue of prisoners, I always raise these issues wherever I travel around the world, and will do so here," said Cameron who was speaking from Cheltenham, Gloucestershire, reported The Independent.
"I want to do it in a way I hope will help the family concerned, and obviously will listen to the concerns of the families and their views before doing these things.
"That is the right way to proceed - to try and help."
Sandiford, 58, from Cheltenham was convicted of smuggling cocaine worth £1.6m from Thailand to Bali in May 2012, and faces death by firing squad.
Sandiford has maintained that she was forced into drugs smuggling to protect her son whose life was at stake.
Indonesia is known for its tough penalties and zero-tolerance policy on drug offences.
Indonesia's President Widodo has defended the country's death penalty laws saying they act as an "important shock therapy" for future offenders.