The firm, which employs 4200 people in more than 70 offices around the world, began a major review in the summer and revealed yesterday it will be consulting with 240 UK employees about their future.
Part of that involves the closure of DLA's Glasgow office, although the firm does intend to keep a presence in Edinburgh.
The Glasgow site is understood to have 10 partners, 25 fee earners and 50 support staff.
A further 10 jobs in the document production unit in Edinburgh are also facing the axe.
DLA said some of those affected by the closure of the Glasgow office may be offered positions in Edinburgh but declined to specify numbers.
The entire document production team, 116 people across eight offices, is being consolidated into one centre in Leeds. Some staff will be offered the chance to relocate.
DLA is trying to find a buyer for its defendant insurance practice, which has 31 lawyers and 19 support staff and is mainly based across Sheffield and Birmingham. Should that fail, it will close the practice down.
A spokeswoman for the firm said: "Following a comprehensive review of our UK business designed to ensure we are operating in a manner, in the locations, and across the practice areas that support both our strategic objectives and the needs of our clients, we have begun a period of consultation in the UK that will consider the possible closure of our Glasgow office, the closure or divestment of our Defendant Insurance Practice and the consolidation into one location of our current multi-site Document Production Unit."
DLA's Scottish offices are headed up by Simon Rae, who doubles up as managing partner and head of corporate. The Herald tried to contact several partners in the DLA Glasgow office but all had been asked by the firm not to comment on the shake-up.
Consultation on the restructuring is due to begin at the end of the month and is expected to be completed by the end of the first quarter of 2013. It is understood trainees will not be affected by the changes and will continue their training at the firm, while those who accept a redundancy package will receive what DLA called "an enhanced scheme".
DLA, then called Dibb Lupton Alsop, moved into Scotland when it acquired the corporate and commercial practice of Bird Semple in 2000.
The legal sector in Scotland has seen a number of mergers in 2012 including Pinsent Masons and McGrigors, and Tods Murray and Fyfe Ireland.
There have also been some job losses. Earlier this year Dundas and Wilson (D&W) announced 28 redundancies after a firm-wide review, while some others, such as Pinsent Masons, have scaled back on support staff during 2012.
However the number of the DLA redundancies is on a level not seen since the first recession caused by the credit crunch.
Then DLA cut around 20 employees in Scotland at a time when other firms also reduced their headcount.
In February 2009, D&W said it was cutting around 50 staff and asked trainees to defer placements, while McGrigors saw around 40 people leave.
The Law Society of Scotland's chief executive Lorna Jack said: "We understand that DLA Piper are consulting with their staff, however it would be premature to comment further at this stage in the consultation.
"If solicitors or support staff would like to speak to the Law Society's professional practice helpline, we have a team of qualified solicitors able to give confidential support and guidance at times like these."