An industry source said the shared services operation, which provides back office functions for the investment banking operation, would be affected by Barclays' plans to make deep cuts in staffing as it looks to return to its roots in retail banking.
The plans will result in Barclays cutting 7,000 jobs in the investment banking arm over three years, meaning demand for some of the work performed by the shared services centre is likely to fall.
The news comes less than four years after plans for the Glasgow centre were unveiled in September 2010.
Barclays expected to create 600 jobs over several years and was awarded up to £6.6m of Regional Selective Assistance funding from Scottish Enterprise.
However, the industry source said: "The majority of cuts are going to be in the front office, expensive bankers in London."
The bank's chief executive Antony Jenkins announced the cuts yesterday after completing his second strategic review since taking over the top job in 2012.
Having announced plans earlier this year to cut 12,000 jobs, Barclays now expects to axe at least 19,000 posts in the next three years.
The additional job cuts will be focused on the investment bank.
A slide in trading revenue due to investor uncertainty and tough post-crisis regulation combined with a string of senior staff departures and a row with shareholders over bonuses have forced Mr Jenkins to take a knife to the investment bank, built up under his predecessor Bob Diamond and once the group's profit engine.
Mr Jenkins said the recent halt in the trading boom was not just due to a cyclical ebb but was partly permanent, as regulators have tightened the screws on large banks in the past 12 months, making some trading activities too costly to pursue.
"We will refocus and resize our investment bank to bring balance to Barclays," Mr Jenkins told analysts and investors. "As currently constituted, it is an unacceptable drag."
Barclays plans to park £400 billion of assets in a new "bad bank".
This will include some of the investment bank's assets in areas like commodities, emerging markets and derivatives.
The investment bank will concentrate on its core markets of the United States and the UK.
The bad bank will also include Barclays' European retail banking operations in Italy, France, Spain and Portugal, and some corporate and Barclaycard assets.
The review will give greater prominence to Barclays' retail operations in Britain, its Barclaycard credit card arm and its African business.
Barclays declined to say how many people are employed in shared services in Glasgow. The company said it employs 3,000 people in Scotland, the vast majority in Glasgow.
The bulk of the employees in Glasgow work in wealth management and in back office work for investment banking.
Barclays had around 1,500 employees in Glasgow when it announced plans for the shared services centre. They worked in existing support operations for Wealth Management and investment banking, investment management and private banking.