Gatherings of over 500 people have been banned since December 26, with this expected to be reviewed after three weeks.
But Prof Leitch told the BBC on Sunday that rescheduling Edinburgh’s Hogmanay celebrations to April may be “too early”.
Following reports that all large gatherings may be banned until April, the Scottish Government has said Prof Leitch’s comments referred only to Hogmanay, and not to wider restrictions.
Asked if it would be possible to hold a rescheduled Hogmanay event in April, Prof Leitch said that while he was “tempted” by the idea, “probably the whole city party might be just a little bit too early”.
Prof Leitch told the BBC: "I like an Edinburgh night out, like any other person in Scotland. I certainly look forward to next year's Hogmanay, now whether we can bring that forward to April or not, I think the jury is somewhat out."
A Scottish Government spokesperson later said the National Clinical Director’s comments did not concern restrictions in general.
They said: “The National Clinical Director was asked about a Hogmanay event taking place in April and was not referring to wider restrictions.
"The legal protections in place require review every three weeks and the First Minister will update Parliament in the coming days on the latest position regarding Covid-19.”
Prof Leitch added that the Scottish Government is “hopeful” based on recently-published data about the severity of the Omicron variant.
"We are hopeful that the data is now aligning. We have now got data from South Africa, from University College London, from Denmark, and crucially from Edinburgh, for the Scottish audience, that suggests serious disease is certainly less with this variant, maybe as much as three quarters less,” he said.
But he added: “Let's put that in perspective, 2,500 Delta cases gets you 50 people in hospital, and we don't take that lightly, that’s a serious problem [...] that means you need 10,000 Omicron cases for the same number of admissions, and Scotland is at 15,000 cases.
"So it's not one jump and you're free. Omicron is encouraging compared to Delta, but Delta was a very, very low bar to be encouraging after.”