It comes after UK Prime Minister Boris Johnson pledged that all adults in the UK will be offered a first dose of vaccine by the end of July, with all those over 50 to receive a jag by April 15.
Asked in the coronavirus daily briefing on Monday if Scotland will be able to keep to that timeline, Ms Sturgeon said she “hopes” so.
The previous target for offering a first dose to all Scots over 50 and those with underlying health conditions – the first nine JCVI priority groups – was the end of May.
"If we have the supplies, we think we can meet the 31 July target to do the whole population,” she said.
"We are waiting on updated supply forecasts to give us certainty that we will have those supplies, or that we can at this stage assume we will have those supplies and therefore say yes, we think we have the supplies to do that.
"What I would say right now is that if we have those supplies we will do that, and that we will vaccinate as quickly as possible.”
She added: “I would hope that the JCVI list, which we have always said [we would offer a vaccine to] by May, I would hope supplies permitting that we could bring that forward to around the middle of April as the Prime Minister indicated, and then the adult population by the end of July.”
The Scottish Government had originally intended to vaccinate all Scots over 18 by spring 2021, but this was later put back.
UK Health Secretary Matt Hancock said on Sunday that the UK Government had enough supply to meet this new target.
"We can see the NHS and all of those partners and all of those working on this have been able to deliver jabs at about half-a-million a day, which is an incredible effort,” he told Sky News.
“So, collectively, the whole team now needs to focus on this renewed target of all vulnerable groups, all those over 50 by April 15 and then we will keep rolling out and make sure that all adults get access to the jab.”