Catherine, 36, made the admission during a live interview with Lorraine Kelly and said it has been "so worrying" seeing them so unwell.
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The former Coronation Street actress said her dad Graham even needed hospital treatment but both he and wife Janet finally seem to be turning a corner.
Catherine said: "This is week three now of them having the virus and it's been a bit of a slog.
"Every time we think they're getting better, they seem to go backwards, but I do feel 100 per cent they've started to turn a corner now.
"Last week my dad got taken to hospital and they said his obs (observations) were OK so they sent him home.
"The nurse said, 'You're going to be much better off at home. We don't feel you're in direct danger at the moment'.
"My mum said to me she's never seen my dad so poorly and it's so worrying because all I want to do is give them a hug."
Catherine added that she has been dropping food parcels at the end of her parents' driveway.
During the interview, Catherine also said she is convinced her hubby, Tom Pitfield, and their five-year-old son Alfie were both struck down with Covid-19 in November.
The Strictly Come Dancing star told Lorraine, via a video call, that the pair fell ill after flying to Dubai from the UK.
Catherine explained: "We travelled to Dubai in November and, when were on the flight, there was a young chap who collapsed several times.
"He was receiving oxygen from the amazing staff on board. We made it to Dubai and he got whisked away.
"The following morning, Tom was in the spare room and he said, 'I can't breathe'.
"He was wheezing, and he's never poorly, so I knew something was really wrong.
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"He got taken to hospital. They thought initially it was some kind of pneumonia.
"By day four Alfie's temperature went up to 40C so we had the paramedics out once again."
The telly star went on: "I revealed this on Instagram once the holiday was over and at least eight people DM'd me and said, ''I was on that flight, and I got it, or my wife got it, or my child go it'.
"So, for me, I think this has been knocking around probably since September or October, and it's gradually been building."
Catherine added: "I've never seen Tom that poorly and he had every symptom of the coronavirus.
"Alfie wasn't as bad, but as we now know it doesn't tend to affect children as badly, in most cases. It's too much of a coincidence."
Lorraine put Catherine's claims to resident TV medic Dr Hilary, but he quashed them.
Dr Hilary told Catherine that the first case of Covid-19 was detected in December 2019, so said it was not possible for Tom or Alfie to have caught it.
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