The presenter, 39, spoke about her mum Linda asking the show's expert what she should be doing to help look after her.
She told Dr Claire: "My mum is older than me, she’s 72, so she’s creeping into that age bracket and my dad.
"As a daughter, because I want to look after them, should I be making sure they’ve got enough food in? But you don't want to add to this panic of stockpiling.
"What does the infrastructure around that look like?"
The doctor reassured Holly that at this stage she doesn't need to be worrying about stockpiling supplies for her parents.
Dr Claire said: "Our chief medical officers say people need to take precautions but they don’t need to isolate themselves.
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"It might not be long until people with underlying conditions may need to isolate themselves and we need to make sure these people are supported."
She went on to suggest having plans in place should close family members become ill, such as sharing phone numbers and deciding who will help do the shopping for anyone who has to self-isolate.
According to BBC News, NHS England has confirmed it is scaling up its capacity to test those who fear they have the bug.
The head service is currently carrying out around 1,500 tests a day, but it will be able to conduct as many as 10,000 daily moving forward.
It means positive cases of the virus can be identified more quickly, helping people to get the treatment they need or take any necessary action.
Most of those who undergo tests will reportedly get their results back in 24 hours or less.
At the time of writing, there are 460 confirmed cases of coronavirus in the UK and six deaths.
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