Linda Bauld, a Professor of Public Health at Edinburgh University, added there is a “real potential” that first doses will also be offered to children under 12.
It comes after UK health secretary Sajid Javid said he has asked the Joint Committee on Vaccination and Immunisation (JCVI) to give advice on strengthening the booster vaccine campaign in response to the new variant, which may be more transmissible than current strains.
The first cases of Omicron, which was initially identified in South Africa, were reported in England on Saturday. No cases have yet been found in Scotland.
In response to the threat, all adults in Scotland may be offered a booster Covid vaccine, Prof Bauld said.
She told the BBC’s Sunday Show: “Israel and a number of other countries are just boosting all adults. It's not age stratified.
"You start with the most vulnerable, but then all adults are eligible.
"That may be what happens here. We will at least go down to the 30s, probably below."
She added that the JCVI will “probably” reduce the waiting period for booster jags, from six to five months after the second dose.
"I think they probably will reduce that gap,” she said.
"If you look at the data from Pfizer's trial, and other countries, reducing it from six to five months seems to me to be proportionate. I think we'll hear that very soon.”
Asked if she would recommend vaccination of primary school children, Prof Bauld said: "Looking at the safety data and the real world data from the US, I think that would be reasonable.
"We have to keep the global context in mind, but there are many parents who are asking for that.
"We'll have more real world data in due course… the JCVI has been very cautious on teenage and young people vaccination, but that does seem to me a real potential future step.”
Vaccination of children aged five to 11 began in the US at the beginning of November.