The former paceman is now isolating at home but feels well.
In line with health requirements, McGrath will miss the Pink Test campaign launch on Monday, as well as the opening two days of the third Test, which commences on Wednesday.
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It is hoped McGrath will recover in time to attend Jane McGrath Day on day three.
McGrath will appear virtually at the SCG on Monday when Australia and England are presented with their special baggy pink caps.
“Glenn has had a PCR test which unfortunately returned a positive result. We wish Glenn and his family good health,” McGrath Foundation chief executive Holly Masters said.
“We are hopeful Glenn will remain well and return a negative result in time to attend Day 3 of the Pink Test, now known as Jane McGrath Day on 7 January.
“We are grateful to our partners at Cricket Australia and the SCG, as well as the England Cricket team and the broadcasters for their ongoing support for the Pink Test and look forward to still making this the ‘pinkest’ Ashes.”
McGrath’s diagnosis follows confirmation that England coach Chris Silverwood has also tested positive for COVID-19, as the case numbers surrounding the Ashes series continue to grow.
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