The cancer campaigner, 40, recently told fans in an emotional goodbye message on Instagram that she had moved to hospice care after battling bowel cancer since 2016.
The mum-of-two had already filmed an episode of the Channel 4 show and told The Sun that she wants it to go ahead.
"I've given my blessing for this episode to run if I'm gone, if it helps save one life it will be worth it," she said.
The star - who has raised more than £7.5 million for charity in the last few days and was recently made a Dame – said early diagnosis of illnesses like bowel cancer saves lives and urged people not to "risk dying because you're shy".
"I might not live to see the episode air but I hope the message to 'Check your poo' will live on, long after I'm gone," she said.
Dame Deborah was one of the hosts of the You, Me & The Big C podcast, which she presented with Lauren Mahon and Rachael Bland, who died in 2018 at the age of 40 after battling breast cancer.
She told her fans on Instagram earlier this month that her body wasn’t “playing ball”.
“My active care has stopped and I am now moved to hospice at home care, with my incredible family all around me and the focus is on making sure I’m not in pain and spending time with them,” she said.
During her final podcast, Dame Deborah said she had gone home to her mum and dad's house as it was where she had always wanted to die.
She has set up the Bowel Babe fund in her name, which will support Cancer Research UK, The Institute of Cancer Research (ICR), The Royal Marsden Hospital and promoting cancer awareness among younger people.
Watch: Dame Deborah James 'gutted' she won't be alive to see her second book published