It comes as the UK Government is set to announce a trial of vaccine certificates to gain access to sporting and entertainment events in England.
The trial will see people able to use an app or document to access after receiving a Covid-19 vaccine, a negative test or natural immunity, having had the virus in the last six months.
Evidence from the experiment will be used to inform a more widespread form of vaccine passports.
Events in the trial will include the FA Cup semi-final at Wembley on April 17, the World Snooker Championship at the Crucible Theatre in Sheffield, and a mass participation run at Hatfield House on April 24 and 25.
The pilots will culminate with the FA Cup Final, again at Wembley, on May 15.
Asked if the Scottish Government is planning a similar trial in Scotland, a spokesperson said the issue is under consideration but questions remain.
"We recognise the potential of vaccine certification for international travel as part of global arrangements, however there are ethical and equity questions to be answered as part of considering using vaccine certification for access to places people visit as part of their everyday lives,” the spokesperson said.
Scottish Liberal Democrat Leader Willie Rennie warned on Sunday that vaccine passports could pave the way for a “permanent ID card”.
Mr Rennie said: “This is super ID cards by the back door. Vaccine passports will divide the country, effectively make vaccination compulsory and pave the way for a permanent ID card.
“The SNP have always been sympathetic to big brother ID cards and tried to introduce a super ID database incorporating information from 120 public bodies.
“Liberal Democrats oppose the use of vaccine passports for accessing public spaces, services and events.
“The best way to keep our country safe is suppress the community spread of the virus by vaccinating almost everyone.”
Ahead of the trials in England, Prime Minister Boris Johnson said: “We have made huge strides over the past few months with our vaccine programme and everyone in the country has made huge sacrifices to get us to this stage in our recovery from Covid-19.
“We are doing everything we can to enable the reopening of our country so people can return to the events, travel and other things they love as safely as possible, and these reviews will play an important role in allowing this to happen.”
First Minister Nicola Sturgeon said on Saturday that a trial of vaccine certificates in Scotland is “possible”.
"I think as all of us desperately want to get back to normal we should absolutely not close our minds to anything that might have a part to play in that,” she told Radio Forth.
"There are big equity and ethical questions - not everybody can be vaccinated, because of some health reasons, younger people at the moment are not currently in the vaccine programme, the vaccines are not authorised for younger people yet.
"We’ve got to be clear about the basis on which we are doing this, and be able to answer some of those questions.”