Speaking on BBC Scotland programme The Nine, the country's National Clinical Director suggested that, while a full house was highly unlikely, there was a good chance that a reduced capacity crowd could be in place for Scotland’s first major tournament appearance in more than 20 years.
Any football matches in the last 12 months in Scotland that have gone ahead with spectators in the stadium have been severely reduced in order to maintain social distancing and even then, games with paying fans have been few and far between in order to help contain the Covid-19 virus.
Asked about the prospect of supporters returning to sporting arenas this summer, Professor Leitch said: "I think with a fair wind; with good restrictions now, if people follow them we will have crowds in Hampden and in other UK stadia in June.
"I’m not sure that will look normal; I think it may well be limited and distanced.
"I actually think UEFA will be more worried now about France, Belgium, Germany and some other countries in the world where the virus is accelerating rather than decelerating.
"And that should be a warning to all of us: that to keep a lid on it, we have to watch how we behave in order to get those crowds.
"I’m looking forward, if I can possibly get in that stadium, to being there.”