Garraway said that she and her co-presenter Ben Shephard were both huge fans of the hit show and that she was disappointed that it was going to be ending with the upcoming fourth series.
"It's very sad to me," she admitted.
"What I've been doing is, my husband is largely bedridden, we have watched everything back from 2018 all over again."
Cox, who stars as businessman Logan Roy, explained that the show was not going to go past its "sell by date", which he said many programmes do.
Draper first fell ill with the coronavirus in March 2020.
He finally returned home to Garraway and their two children - 16-year-old daughter Darcey and 13-year-old son Billy - over a year later in April 2021.
'Has Brian become a little bit more Logan or has Logan become a little bit more Brian?' - @benshephard
Legendary actor Brian Cox talks to Ben and @kategarraway about the comparisons between himself and his Succession character. pic.twitter.com/IEhMUeVWTO
— Good Morning Britain (@GMB) March 24, 2023
In December, the TV star said on ITV's Lorraine that it was a "long onslaught" and that Draper had some "better days" and some "worse days" as his fight went on.
"I think it’s very tough on him and it’s very tough on the people around him," added the broadcaster, who married the former political adviser in 2005.
Watch: Matt Hancock grilled by Kate Garraway on GMB