The city council's powerful executive committee normally sits in one of the grand rooms in the City Chambers.
Its members includes council leader Gordon Matheson, deputy leader Archie Graham and City Treasurer Paul Rooney, the executive spokesmen for the services the council provides.
They are joined by SNP leader Graeme Hendry, Green Party leader Nina Baker and a number of their political colleagues.
On Thursday, the council is expected to agree the committee should move from the City Chambers to sit in venues across the city.
These are likely to include the Bridge, in Easterhouse, Scotstoun Stadium and Langside College.
The aim is to encourage more members of the public to attend meetings and increase transparency.
It is hoped the first meetings outwith the City Chambers will take place in the Bridge, in Easterhouse, in April, with further public meetings in June and August. A rolling programme of meetings will then be drawn up.
Mr Matheson said: "The proposal aims to increase transparency and raise awareness among the public of both local and city-wide issues of importance to residents and their communities.
"Each meeting will provide an opportunity for the executive committee to engage with communities, meet a range of stakeholders and discuss the proposals for implementing the council's strategic plan."
Area committees of the council regularly meet in neighbourhood venues but this is the first time such a major council committee has embarked on a tour of communities.
Councillors may also visit local projects and initiatives following their meetings.
Councillor Matheson added: "Decisions will be taken in the heart of the communities which they affect and l ocal residents will find it easier to see the council in action."
The scheme is similar to that of the High Court, which leaves Edinburgh to sit in Sheriff Courts across Scotland on a rota basis.