It comes as nearly a third of Scotland’s adult population – 1,465,241 people – have received a first dose of the vaccine.
But figures announced by the First Minister recorded the lowest daily first doses on Monday of any weekday since January 18.
Just 19,753 first doses were recorded, amid an expected drop in vaccine supply from Pfizer and a ramping up of second doses – with that daily figure at 5,861, by far the highest so far.
Announcing a route map out of lockdown for England on Monday, Prime Minister Boris Johnson said vaccine certificates would be the subject of one of four studies conducted as part of easing of restrictions.
Asked about vaccine certificates on Tuesday when giving a statement to MSPs on Scotland’s route out of lockdown, Ms Sturgeon said she would not “close her mind” to the idea.
"There may be scope for vaccination giving you the ability to do certain things that without vaccination you might not be able to do,” she said.
Scottish Liberal Democrat leader Willie Rennie called for clarity on the idea. He raised concerns that vaccine passports may contribute to inequalities between those who have been able to get the vaccine and those who have not.
"In the past the First Minister was sceptical about vaccine passports,” he said. “Now she has left the door open for their use.
"I am concerned that vaccine passports are slowly gaining traction, but we don’t want a two-tier society which would exacerbate inequalities.”
Ms Sturgeon said the concept of vaccine passports “means different things” to different people, and the idea would need to be further considered. She said she would not support people being denied access to certain services because they had not had a vaccine.
"There are a lot of things we need to think through,” she said.
"We need to firstly understand … exactly what vaccination gives you in terms of protection against getting or passing on the virus, and then we need to think about these ethical issues, about what is it reasonable to say can be accessed with a vaccine certificate and what isn’t.”