There were crowds of over 10,000 at four of the six Scottish Premiership matches over the weekend
The joint response group representing the Scottish FA and SPFL "warmly welcome" the likely introduction of spot checks for vaccine passports.
The government scheme will come into force from 1 October.
Those over the age of 18 will be required to show they have had both doses of vaccine to attend matches with a crowd above 10,000.
First Minister Nicola Sturgeon has urged venues to use "common sense" with a "reasonable number" of checks.
Scottish football authorities had warned that comprehensive inspections would be unworkable.
"We have been in detailed discussions with Scottish Government officials in the past few days as we seek to develop a workable and proportionate methodology," read a brief statement from the JRG.
"There remain a number of aspects which require to be finalised but we are hopeful that our positive talks will bear fruit and that Scottish football will continue to play a prominent role in reducing the impact of the virus."
Those working at matches, people who cannot be vaccinated for medical reasons and vaccine trial participants will also be exempt.
Ms Sturgeon told MSPs that Covid-19 cases had fallen in Scotland in recent weeks, but warned that "the position remains fragile" with the NHS under "sustained pressure".
