Her statement comes after the Joint Committee on Vaccination and Immunisation (JCVI) was asked to consider advice on increasing vaccine coverage in response to the new Covid variant Omicron.
The committee has advised on booster vaccines for all over-18s.
Some experts have also called for vaccines to be offered to children aged five to 11, as is the case in countries including the US, Canada and Israel.
Devi Sridhar, professor of public health at Edinburgh University, has repeatedly recommended vaccines for younger children.
She said on Monday that it would be “irresponsible” to leave youngsters vulnerable to the new variant while so little is known about Omicron.
Prof Sridhar wrote on Twitter: ”We should be offering parents the choice of vaccinating 5-11s as quickly as possible in the U.K. Leaving them completely exposed to a new variant (when data is limited) seems irresponsible. Esp since millions of kids 5-11 already vaxxed in the U.S.”
Asked about Prof Sridhar’s comments in a media briefing on Monday, Ms Sturgeon said she “agreed with the sentiment”.
“My view … it should be a caveat that I’m a politician, not a clinician,” Ms Sturgeon said.
"I want to get the vaccine to as many people as I possibly can, so in that respect I’m with Devi on the sentiments of what she is saying there.
“Obviously we have to make sure the vaccines are approved, and then politicians like me have to follow clinical advice on who is and is not appropriate to receive a vaccine.”
Scotland is ready to scale up the booster vaccine programme if needed, Ms Sturgeon said.
“Over the weekend we have already been starting to consider the operational aspects of that,” she said.
“We are already going very, very fast in the programme, we’re the most vaccinated part of the UK. We are already trying to step that up."