Customer relations staff who handle complaints at the firm's Cadogan Street "centre of excellence" are believed to be in the firing line.
It is understood staff at the call centre will be axed by the end of this month with their work transferred to three of four other sites south of the border.
Direct Line, which also owns the Churchill and Privilege insurance brands, along with the Green Flag breakdown service, employs about 1000 people in Glasgow and Rutherglen, where there are expected to be additional cuts.
One company source said: "Staff have accused bosses of being secretive and not telling them anything about the job losses.
"Some have already been trying to get jobs at other call centres in Glasgow."
In June the company confirmed 2000 jobs across the UK were at risk, including 150 in the central belt.
A spokeswoman for Direct Line said it would not be releasing any further statements about the Scottish job losses and would not confirm the exact number of posts to be shed in Glasgow and Lanarkshire.
The company said previously it hoped to redeploy staff where possible and find opportunities for affected workers with other potential employers.
It has already axed 1200 jobs since last August under a plan to make annual savings of £130 million a year.
The firm has 16 sites across the UK, including offices in London, Croydon, Bromley, Leeds and Manchester.
Direct Line, which was spun out of Royal Bank of Scotland (RBS) when it floated on the stock market last year, recently revealed £94.3m profits for the first three months of 2013
Taxpayer-backed RBS floated Direct Line on the stock exchange to appease European Union rules on state aid. RBS still owns 48.5% of the insurer but must sell its entire stake by the end of 2014.
The company was set in 1985 with just 63 employees. There are now more than 10,000 employees across the UK
Direct Line started with just one call centre in Croydon and went global in the 1990s, selling car insurance policies in Italy and Germany