Mr Draper remains in hospital after being diagnosed with coronavirus in spring 2020.
The 53-year-old was admitted to hospital with the virus in March.
He no longer has coronavirus but continues his recovery in hospital.
Speaking to Good Housekeeping magazine, Ms Garraway, a Good Morning Britain host, said she has been receiving support from the Cambridges.
She said: “It’s wonderful that they even know who I am and what I’ve been through.
“They were so sweet to me and showed their compassion to Darcey and Billy.
“Because they imagined what it would be like for their own children.
“And Prince William knows exactly how hard it is to be without a parent and how it can affect you, so he shared his thoughts on that.”
READ MORE: Ranvir Singh offers invaluable support to Kate Garraway over children
Darcy, aged 14, and Billy, 11, are Kate and Derek’s two children.
Ms Garraway also claimed Prince William said he’d like to hug her if it wasn’t for social distancing rules.
She also explained how much the royal intervention meant, stating: “Of course, they have a privilege and protected life compared with many of us, but it was a reminder that the loss of people you love and care about is something that unites us all.”
READ MORE: Kate Garraway says ‘not sure I’m coping’ as she gives Derek update
On Friday, the UK vaccinated another 487,756 people, the second highest daily total.
In total, more than 12 out of every 100 people in Britain have received their first jab, a figure far higher than in the European Union.
Coronavirus has killed over 104,000 people across the UK, the highest figure of any European country.
The Duchess of Cambridge has also released a warm video message to parents struggling during the coronavirus pandemic.
The 39-year-old mother of Prince George, seven, Princess Charlotte, five, and Prince Louis, two, told parents to “look after” themselves during this “hugely challenging time”.
In the address, due to be released later on Sunday, the future queen spoke about the need “to be the very best versions of ourselves for the children in our care”.