Shephard has tweeted his thanks to viewers, on behalf of his co-host Kate Garraway, for their support during her husband's battle with COVID-19.
Draper was hospitalised at the beginning of April for coronavirus and admitted to the intensive care unit, where he was put into an induced coma.
"Thank you for all your messages to Kate, Derek, Darcey and Billy", he tweeted.
"He is still critically ill but @kategarraway really wanted us to share her thanks for your continued support and to send her love to everyone who has family members who are ill."
Ms Garraway, 52, has not made any public statements on her husband's condition since last Thursday (April 23), when she praised NHS staff for "keeping my Derek alive".
"He is still critically ill in intensive care, but where there is life there is hope," said the presenter on Instagram, adding, "Thank you #nhs from the bottom of my heart".
A week earlier, on April 17, she said: "From the bottom of my heart, a billion thank you's to the extraordinary #nhsworkers whose skills, dedication and downright guts in the face of so much personal risk, are keeping my Derek alive, just as they are doing for thousands of COVID patients.
"I’m afraid he is still in a deeply critical condition, but he is still here, which means there is hope."
Mr Draper, 52, has been in hospital since early April. The couple have two children and have been married since 2005.
Born in Chorley, he was educated at Southlands High School where he graduated in 1984 before attending Runshaw College in Leyland.