An interview with the ITV presenter by Piers Morgan on the final episode of his Life Stories series will air on Sunday evening, in which she discussed her personal life and Draper's health progress.
Garraway said: "It's moments like that which make you realise he is there, and we have had others.
"He will turn to me and say 'I love you'. He is there, he has fought so hard to stay in this world, and I'm not giving up on him, ever.
"He will have moments of clarity, then it's like he disappears but then he finds a voice," she added.
Last month, Morgan wrote in his column for the Daily Mail that he was "stunned" to hear Draper's voice on the phone the night before he was set to film the interview with Garraway.
He said that the former political adviser was able to say "hello" and "thank you". Morgan wrote that he had "assumed [Draper] wouldn't be capable of any kind of proper conversation, given his condition".
Draper fell severely ill with coronavirus in March 2020, and was placed under a medically-induced coma. He woke up several months later, and was only able to go home more than 12 months after he was admitted to hospital.
He now requires round-the-clock care at home, provided by Garraway and a team of healthcare professionals, as his recovery continues.
Garraway described Draper's illness as feeling like she "walked through a fiery furnace, or fell down a rabbit hole".
She told Morgan: "The world went dark and I'm still looking for the light at the end of the tunnel.
"Covid has devastated him, from the top of his head to the tip of his toe. His digestive system, his liver, his heart, his nervous system.
"We're pretty sure the inflammation did pass through his brain. Fundamentally he is in a terrible state, but look: he's alive."
Garraway will replace Morgan as the host of Life Stories after tonight's episode, after the former Good Morning Britain presenter recorded more than 100 episodes of the ITV series.
The interview will air on ITV at 8pm on Sunday 5 December.
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