The campaign to honour frontline workers is gathering momentum and Andy Street believes the George Cross would be suitable recognition for those putting their lives on the line.
The Mayor said the coronavirus pandemic was the NHS' "finest hour" and that they deserved to be recognised for their bravery.
He said: "These are unprecedented times, but awarding this medal collectively, to thousands of people for their joint endeavour, has been done before.
"In another echo of World War Two, we must look back more than 70 years to find a fitting precedent.
"In 1942 the George Cross was awarded to the island of Malta by King George, so as to "bear witness to the heroism and devotion of its people" during the great siege they underwent in the early part of the Second World War.
"Six years after Malta received the George Cross, the NHS was founded. After seven decades of devoted service to the British people, NHS staff now find themselves under siege too, from coronavirus. There is no doubt in my mind that this is their finest hour.
"It is time to reflect the unique contribution to our society of the NHS, and the gallantry shown by its staff. The National Health Service has earned the George Cross."