Figures have been on the rise in recent weeks, with at least new 3,000 cases recorded every day for the last five days and a positivity rate that peaked at 12.4% on Monday.
The rise coincides with the further easing of restrictions in Scotland, which took place on August 9.
But Prof Leitch said that he does not expect major changes to be made on Tuesday when the First Minister speaks at a coronavirus briefing in Edinburgh.
In the past week, case figures have more than doubled, from around 10,000 to more than 21,000.
“We are concerned,” he said on BBC’s Good Morning Scotland programme today.
“It’s principally young people, but not only young people.
“But a big percentage are under 40, so that means the harm is not as significant, but people are still harmed by this virus, either the older people who get it or some small proportion of those younger people.”
Hospital figures have also stagnated in recent weeks, with the same number (356) in hospital on Monday as compared with the day restrictions were eased in Scotland, although the figure has risen from 312 on Friday, adding another 18 on Monday.
When asked about the possible return of restrictions because of the rising numbers, Prof Leitch said: “Cabinet will meet today and we’ve given balanced advice, we’ve told the truth about the state of the pandemic.”
When asked if restrictions could be imposed as early as Tuesday, he said: “I don’t expect us to make dramatic changes, I think we will almost certainly keep the baseline mitigations that we’ve got in place just now.”
Last year, the return of schools and universities was contributing to a spike in cases which culminated in a nationwide lockdown by Christmas, but when asked about clusters in schools, Prof Leitch said: “No, we’re not seeing specific examples of outbreaks.
“There are a few, connected to events usually, indoor events, people gathering in houses or people at weddings, or pubs or restaurants.
“It’s depressingly predictable.
“We’ve known about this virus for 18 months, we learn more everyday, but fundamentally this virus spreads when people gather indoors with no ventilation too close together, it’s as simple as that.”
He added: “We have had some school cases, I’m not suggesting that doesn’t happen, of course it does, but we’re not seeing massive numbers and we know how much education has been disrupted so we’re keen to see that get back.”
In terms of the return of universities, Prof Leitch said that he was confident in being able to handle students heading back to campus by encouraging those in the UK to get vaccinated and test before they arrive, while overseas students have to quarantine if they are from high risk areas.
In recent weeks, Prof Leitch said, 40% 16 and 17-year-olds in Scotland have now received their first vaccination.