Scottish Rugby has submitted a proposal to have 5,000 fans at Murrayfield for Edinburgh's meeting with Glasgow on 2 January, with plans for the number to rise to 25,000 for the Six Nations.
In between, the organisation wants the Scottish government to allow up to 10,000 fans for a club game.
No submissions have been made about Glasgow fans returning to Scotstoun because of higher rates of Covid-19.
The union has forecasted potential losses of £18m by May.
"We believe we are ready as soon as the government allows to welcome spectators back to our venues," Scottish Rugby said in a statement.
Murrayfield hosted 700 fans for a Pro14 between Glasgow and Edinburgh in August as part of a pilot event.