The MP and his wife, Rose, are self-isolating at their home near Ellesmere and he admitted today he was feeling "very groggy".
However, Mr Paterson said that he hoped his illness was the virus so that he would then have an immunity and be able to help more with the crisis.
He said he was continuing to work, through video conferencing and the telephone.
The MP tweeted to say he was displaying some of the symptoms.
Speaking from his home he said: "I do feel very groggy and I have a cough. Rose and myself are now holed up for the next 15 days.
"I am going to push through it with paracetamol and lots of water.
"Bizarrely I hope it is Coronavirus, particularly as I feel so unwell. At least if I can show that I have had the virus I will have an immunity which could really be an asset. I could get out and about helping knowing that I don't pose a risk to anyone."
He said he would still be chairing Friday's Health for Oswestry group, online
Mr Paterson said he would not be surprised if he and other MPs had contracted Coronavirus.
"The House of Commons is not a great place for spreading germs," he said.
"Someone working on the same floor as me believed she had contracted it last week and I immediately sent my staff home to work. We are all working remotely, but we are all still working for the constituency with regular conference calls."
"I am liaising with Shropshire Council and ensuring that we can help those who are emailing me."
He also received support from Shrewsbury's MP Daniel Kawczynski, who tweeted: "Wishing you a speedy recovery neighbour. Am operating from my Commons office and my hard working team from their homes. If you or your team need any assistance please let me know."