The trust which runs Glasgow's civic sports and culture facilities will confirm the reduction at a meeting of its board next week. It claims the changes better reflect usage.
Glasgow Life also insisted that, unlike in other parts of the UK, there were no plans to shut any of its 33 libraries and that the changes will see cash invested to help benefits claimants deal with welfare reform changes, a recent additional service.
However, opposition politicians said they feared the move was the "thin end of the wedge" over cultural and sporting facilities and called for consultations before the changes were implemented.
Union leaders also said that they were sceptical over any change to reduce library opening hours.
The most affected will be Gorbals library, which will lose 12 hours, while Bridgeton and Cardonald will each see their current weekly hours reduced from 53 to 48.
The raft of other libraries which open 51 hours-per-week will all lose three hours, as will those facilities currently operating for 45 hours.
Only Hillhead in the west end will see an increase, gaining an additional hour, but with some later openings.
The libraries at the Gallery of Modern Art and The Bridge complex in Easterhouse will retain their 60-hour weeks.
A report on the proposal states: "We are confident that, based on usage levels at the times we are planning to change, customers will quickly become used to the revised opening hours and will match their visiting times to suit.
"In the medium term, we anticipate that service levels will show virtually no reduction. Indeed, we are confident service enhancements will increase activity in the community libraries."
However, the opposition SNP in Glasgow said it had concerns over the impact on the elderly, who often frequent libraries early in the morning, as well as increased costs of admission to and hire of Glasgow Life sports facilities.
A spokesman said: "We will be watching these proposals carefully. We have concerns that this could be the thin end of the wedge and there may well be more to come from Glasgow Life.
"We want assurances that they will be consulting communities and service users before any decision is taken."
One Labour source in the city said: "It's better than actually closing libraries altogether but a few folk have raised concerns that it is yet another battle with Unison if they get upset by it.
"The officers assured us the policy is cost neutral in that any staff cost savings will be redeployed to other places where it is busier."
Unison said it was considering the proposals, which are expected to be implemented by April.
A Glasgow Life spokesman said: "We are standardising library opening hours across the city.
"There will be no library closures and none are planned. Any staff resource freed up by the new opening hours will be reinvested in new or improved services which reflect customer needs.
"In particular, we will be providing substantial support for the welfare reform changes. All benefit claimants will have to make and manage their claims online."
In the last year, Glasgow's library service registered 5.5 million visits and 1.1m usages of PCs and wi-fi across the city.