Dalglish was hospitalized on Wednesday for treatment for an infection after suffering from a problem with gallstones.
As a new hospital admission, the 69-year-old received a routine coronavirus test which returned positive despite the fact that the Reds had no symptoms.
Dalglish has since been released from hospital and is now recovering from his own isolation at home.
And, writing in the Sunday Post, he praised the efforts of NHS staff across the country in response to the ongoing coronavirus epidemic.
“I would just like to thank the doctors, nurses and all the staff for taking care of me,” he said. “They were absolutely great.
“People may think the name Dalglish brought me in and gave me the best care. But no.
“I was taken care of because NHS staff treated everyone the same. They consider everyone to be human. Names and background do not fit there. This is how it should be …
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“As a nation, we are all very fortunate to have them and I wish them good luck as they work tirelessly to help the country weather this pandemic.”
Dalglish scored 172 goals in 515 appearances for Liverpool, then led them to three championships as a manager, including their most recent in 1990.