Draper is in a coma after a near-fatal battle with coronavirus, which began in March, and the TV presenter previously revealed she has only been allowed to talk to him over video call up to now due to quarantine restrictions.
Garraway told GMB viewers as she returned to work for the second day since Draper fell ill: "I might be able to go and visit Derek after the show today and in fact the nurses are going to put Good Morning Britain for him today.
"They’ve got a TV and they’re putting it on this morning, obviously we don’t know what he can hear or see.
"They didn’t realise I was on air yesterday, but they’re going to put it on today and see if there’s any reaction. We’re trying anything at the moment."
The 53-year-old breakfast show host added: "And apparently we haven't got anyone on autocue either."
Co-host Ben Shephard explained: "Someone has stepped in but our autocue operator has overslept.
"Maybe they had the same driver as you. Who knows what we'll be saying. But it's lovely to have you here."
Garraway and Shephard, 45, have taken over hosting duties on the ITV morning show as Piers Morgan and Susanna Reid began their summer break.
After hosting her first live show in four months on Monday June 13th, Garraway wrote on Instagram: “Well I survived my 1st day back without crashing the show thanks to the brilliant @benshephardofficial , the whole wonderful @gmb team & all of YOUR patience!! Thanks so much for your incredibly kind messages. Means such a lot . Derek had a stable day too so 🤞🤞🤞🙏🙏🙏. See you at 6 a.m tomorrow xxx”
Speaking about 52-year-old Draper’s condition on GMB last week Garraway explained he is in a “minimal state of consciousness”. But while he opens his eyes as she talks to him over Facetime, she has no idea if he can see or hear her.
The TV presenter – who took part in I’m A Celebrity... Get Me Out Of Here! last year – revealed she and her children son Billy, 10, and daughter Darcey, 14, have not been allowed to see their father in person or give him a hug.
She said: “I’ve been fighting to do that, but I'm respectful of what the doctors say.
“I said you can now shop in Primark, surely I can give him a hug?! And they say we’ve got to be careful. But I’m hoping we can do that soon.”
Garraway and Draper, 52, have been married since 2005.