The additional hour, available to around 225 premises, is expected to be implemented before the end of the year and brings the city's licensing laws into line with those of Edinburgh and Aberdeen.
Licensing chiefs say the 1am plan is due to changing socialising habits and the reluctance of older pub customers to continue their evening in nightclubs after midnight. The additional hour, they said, would not necessarily equate to more people consuming more alcohol.
Alcohol-awareness charities have largely welcomed Glasgow's draft policy, but warned that increasing availability of liquor could have detrimental impact on health and communities.
The policy would also see the scrapping of the seven areas across Glasgow currently designated as "over-provision zones", essentially areas including parts of the west end and city centre considered at saturation point with licensed premises.
Instead, it has created new areas across the east end and south side using data on the volume of licensed premises, alcohol-related hospital admissions and crime statistics, as well as the multiple deprivation index,
Other proposals now out for consultation include relaxing the 10pm curfew for outside drinking at venues where the impact on residential properties is not a major factor.
Early morning licences for pubs claiming to serve alcohol to shift workers and market traders, providing it is served with a meal, is out, although venues already opening at 8am will not be forced to open later unless caught breaching their conditions.
The handful of nightclubs outside of the city centre face being given an extra hour's opening, partly on the back of arguments to maintain late night vibrancy in outlying town centres.
Hybrid premises, which operate as bars and are permitted to stay open until 3am if they provide entertainment, face being tightened up, with council officials ramping up the monitoring of the "entertainment" on offer.
Casinos offering what amounts to an after-hours club with alcohol available until 6am can also expect a clampdown.
Meanwhile, the local authority is consulting on its policy for licensing hours during the 2014 Commonwealth Games. The consultation document reads: "The licensing board is aware there are a variety of different opinions as to whether additional licensed hours are consistent with the city's legacy aspirations of providing momentum for people to become more active and adopt healthier lifestyles while at the same time helping to keep businesses moving forward through tough economic times."
The pubs being offered the extra hour will be within the area bordered by the M8, the Clyde and High Street to the east, with the expectation not all will take up the offer and those which do largely on a weekend-only basis.
Sources insist some academic evidence points to customers basing their alcohol consumption on cost rather than time available, and reference the problems caused on the streets by people bingeing in bars when pubs shut at 10pm.
Malcolm Cunning, chairman of the Glasgow Licensing Board, said the plan had widespread support. He added: "We regard 1am opening for city centre bars as a sensible compromise for those who wish to stay out a little later but who do not want to go to a nightclub to do so."
Dr Evelyn Gillan, chief executive of Alcohol Focus Scotland, said: "We welcome the fact the board recognises the link between the number of alcohol outlets and the level of alcohol-related problems in an area."