Up to 10 roles are likely to go from Direct Line's Glasgow office, as the insurer spun out of Royal Bank of Scotland cuts 236 jobs across UK operations as part of its drive to cut £100 million of costs.
Direct Line, which has already announced more than 900 job losses, said the latest cuts would affect its commercial, risk, and customer divisions.
Paul Geddes, chief executive of Direct Line, said: "These proposals are another important step on our journey to deliver on our cost-saving target.
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"They are essential to ensure we are as efficient and competitive as possible."
Direct Line, Britain's biggest motor insurer, reported in September that it had achieved about 50% of the planned cost cuts.
It said a further 20% will be achieved by cutting marketing spending, and plans are being finalised for the remaining 30%.
A spokeswoman for Direct Line said that most of the job cuts will come from its bases in Birmingham, London, Leeds and Maidstone in Kent.
But she said "five to 10" posts are likely to be lost in Glasgow.
The company has an office on Cadogan Street, which largely operates as a call centre.
Its presence in the city is much scaled back after the decision two years ago to close its operation at Atlantic Quay and pull out of offices on St Vincent Street, at the cost of 440 posts.
At the end of last month Direct Line announced plans to cut 70 "senior leadership" roles.
Royal Bank of Scotland sold 30% of Direct Line's shares in October as part of a three-stage programme to offload the company.