John Swinney, addressing the Scottish Parliament, said the nature of the measures to be brought in for Scotland would depend on the decisions made by the UK Government later on Tuesday.
He said the Scottish Government had “engaged” with the UK Government "for some time”, but has “not yet been sighted” on the exact plans coming from Downing Street.
Mr Swinney said the decision from the UK Government on the nature of the measures had been deferred to this evening.
A UK Government press conference is set for 5pm this evening.
The deputy first minister said the extent of the measures in Scotland would depend on the severity of the UK Government measures.
He said if the UK Government introduces measures “at a minimal level”, the Scottish Government would look to introduce more stringent restrictions to stop Covid-19 being imported into Scotland.
Mr Swinney said: “We have engaged with the UK Government for some time on improving border controls, and, while we have had some discussions on issues such as quarantine hotels, we have not yet been sighted on what the UK Government intends to announce or when it intends to announce it.
“I understand that decision has been deferred to this evening. Border controls will work best on a four-nation basis.
“Otherwise – for example if Scotland establishes a supervised quarantine regime, and England does not – that could be problematic if unrestricted travel between Scotland and England resumes.”
Mr Swinney said quarantine hotels could form part of such a regime, confirming Scotland would go “at least as far” as the UK Government.
Quarantine hotels could see passengers arriving into Scotland transported from airports to hotels to spend their full 10 day mandatory isolation away from the general public.
This system is used in countries such as Australia where the person travelling must pay for the hotel should they be required to use the hotels.
It is viewed as a way to limit the potential for Covid-19 to be imported into a country without being noticed due to asymptomatic transmission or people breached quarantine restrictions.
The deputy first minister said: “The Scottish Government believes that a comprehensive system of supervised quarantine is required. And so I can confirm that the Scottish Government will initially go at least as far as any UK Government announcement in enhancing quarantine arrangements, including through the use of hotels.
“However, if these UK restrictions are at a minimal level, we will look at other controls we can announce, including additional supervised quarantine measures, that can further protect us from importation of the virus, and we will set those out next week.”
Last week, transport secretary Michael Matheson said the proposal for quarantine hotels was being considered alongside a “suite of measures”.
First Minister Nicola Sturgeon said on Monday at her daily coronavirus briefing the proposal was “under active consideration”.
She added: “If there is a decision at any stage to proceed with this kind of policy, it’s important we learn from other countries, but that we put in place a model and system that is right for our circumstances here.”