Mr Gutwein has targeted a 90 per cent full vaccination rate for people aged 16 and over by 1 December.
He said Tasmania was "on track" to reach the number and aiming to reopen by Christmas.
He reiterated he wouldn't reopen until all eligible Tasmanians had the chance to be vaccinated and any border decision would be made on public health advice.
The national plan out of COVID-19 aims for easing of restrictions at 80 per cent, although state borders aren't specifically mentioned.
"The reopening of our borders is what we're considering. Other states are considering the reopening of their communities. That's the difference we have in Tasmania," Mr Gutwein said.
"As we move to reopen our borders, Delta will arrive. And when Delta arrives some people will get sick, some people will get very sick and unfortunately, some people will die.
"What we need to do is to get to a point where I can confidently say to myself that every single Tasmanian that is eligible has had the opportunity to have the vaccine."
Queensland last week indicated it would watch NSW closely before deciding whether to open for Christmas.
Tasmania has had just one case this year, a NSW traveller who tested positive while in hotel quarantine.
Mr Gutwein said the state was mulling border entry requirements, such as tests prior to entry, allowing only fully vaccinated people in, and short quarantine periods for some arrivals.
The state government has commissioned Tasmania-specific modelling, to be released in mid-October.
The island state is closed to Victoria and NSW, its two biggest domestic tourism markets, as well as the ACT and New Zealand.
Almost 58 per cent of Tasmania's eligible population has been fully vaccinated, behind only the ACT and NSW.