Nicola Sturgeon said a decision on measures will be made after a Wednesday morning cabinet meeting.
Marston's operates 21 sites in Scotland, of which eight are currently closed amid curfews on hospitality industry.
Strict new measures will come into effect on Friday for pubs, restaurants and cafes across Scotland.
A closing time of 10pm came into force for pubs and restaurants in Scotland on Friday.
The Scottish Hospitality Group has warned the sector is already 'on life support' with 90,000 jobs at risk.
The First Minister says Scotland will stay in phase three of its lockdown exit strategy 'for some time yet'.
There is some Covid-19 transmission in the city's hospitality sector, the First Minister said.
The initiative which sees the UK Government foot 50% of diners' bills has not been extended into September.
The First Minister said failing to follow guidelines could lead to outbreaks of coronavirus.
Hairdressers, nail salons, dentists, hotels and shopping centres will also open their doors in coming days.
Half-price meals will run at participating restaurants from Mondays to Wednesdays next month.
The prince praised the country's 'entrepreneurial spirit' in a video message in support of the industry.
The tourism and hospitality sector has been asked to prepare for reopening on July 15.
The National Union of Students is calling for greater support for students who have lost part-time jobs.
The Scottish Government said the coronavirus outbreak is an 'economic emergency'.