A Police Scotland spokesperson said: “Planning is under way for a potential visit to Scotland by the Vice President of the United States.
“Details of any visit would be for the White House to comment on, however it is important that we prepare in advance for what would be a significant policing operation.”
Vance and his family were in Kent last week, where they stayed at Chevening House, the official residence of the foreign secretary, before spending time in the Cotswolds.
On Friday he raised questions about the UK’s plans to recognise a Palestinian state, during a meeting with Foreign Secretary David Lammy.
The two men also went carp fishing together.