The FM said she has heard 'very loudly' criticisms from airport bosses over the issue.
Scottish aviation bosses say the 14-day quarantine policy has already cost thousands of jobs.
Health Secretary Jeane Freeman says staff don't have security clearance to access passenger details.
Boris Johnson claimed there is 'no such thing' as a border between Scotland and England.
The First Minister said she thinks there should be more discussions between leaders on a four-nations basis.
Passengers arriving into the UK must self-isolate for 14 days, with a £480 fine in Scotland for breaching quarantine.
Justice secretary Humza Yousaf confirmed the policy will begin from Monday as part of measures to fight Covid-19.
Boris Johnson said a 14-day quarantine for new UK arrivals could help prevent a 'second peak' of Covid-19.