Additional subway branches will be considered as the city waits to hear whether it will host the Commonwealth Games in 2014.
Strathclyde Partnership for Transport submitted proposals to the council last week. These would see tunnels and viaducts from former rail links reused by lighter subway trains.
Financial advisory firm Grant Thornton will carry out a feasibility study on the plans and is due to report back within three months.
A more ambitious proposal for an "eastern circle" subway extension was turned down on the grounds that, at an estimated cost of £2.3 billion, it would prove too expensive.
Councillor Alistair Watson said: "There is potential to use Glasgow's legacy of disused railway infrastructure, but we must ensure that any solutions provide the public with good value for money.
"The decision on the host city for the 2014 Commonwealth Games is expected next month. If Glasgow is to be successful this will have to leave a lasting legacy."