Glasgow City Council is expected to approve a £500,000 grant towards the project to expand the venue, which has become a victim of its own success.
The lack of space has particularly affected GFT's international ambitions for the Glasgow Film Festival – a hugely successful event and the third largest of its kind in the UK – which currently has a revenue return of £7.85 for ever £1 invested.
According to a new report, "being limited to only two screens puts GFT and Glasgow's moving-image industry at a significant cultural, social and economic disadvantage compared to other cultural cinemas in UK cities such as Edinburgh, Manchester and Bristol".
The plans would see the existing cafe converted to create a new 60-seater cinema and a new cafe developed at the rear of the building.
As well as these works, an additional £390,000 will be spent at a later stage refurbishing education suites and offices, bringing the overall cost to almost £2m.
Creative Scotland and the GFT's own reserves will pay for the bulk of the remainder of the costs, with the council claiming its support is justified under investment in the arts and cultural industries.
The addition of a third cinema screen, which is expected to be open at the end of 2013, will help the GFT meet these demands and also increase its education and outreach work.
Once completed, the extra screen will also allow for 1500 new programming slots or opportunities a year, a 50% increase, and a potential uplift in custom in the first six months of operation of an additional 16,800 admissions.
The report, to be tabled at this week's meeting of the council's executive committee, states: "GFT has worked in a creative and successful partnership with the Council of Glasgow since GFT's inception in 1974.
"The last time GFT sought and received major capital support from the council was in 1990 for the creation of Cinema 2.
"This led to GFT becoming the success story it is today, as one of the UK's most successful cinemas and a leading member of the Europa Cinemas network. An investment by the council of £500,000 in GFT for Cinema 3 will expand a unique asset of the city, yielding significant levels of return on investment – economic, cultural and social – to help the city prosper."
Council leader Gordon Matheson said: "We have to ensure we continue to support and give a platform to new talent coming into Scotland's film and television industry. This is a vital part of the work of the GFT, which is one of the UK's most successful cinemas.
"I am also very aware that the work of the GFT through its learning and outreach programme has helped to inspire and educate many generations of Glaswegians to cultivate a love of film and film making."
Jaki McDougall, chief executive of Glasgow Film Theatre, said: "With admissions to GFT of over 200,000 in the financial year 2011-12, our two cinemas welcome more than twice the UK screen average admissions. Glasgow Film Festival is the fastest-growing film festival in the UK with admissions in 2012 of over 35,000 and, with GFT as its hub, a new cinema screen would allow us to increase our festival audiences as we look towards our 10th anniversary in 2014.
"The addition of Cinema 3 would create up to 1500 new screening slots per year, which will allow us to continue to diversify our cultural programme whilst also providing youth activities including a home for the Youth Team who curate Glasgow Youth Film Festival."