QTS hopes to clinch a deal under which it will supply rail robots to automate work involved in keeping the hundreds of miles of track that cross the sprawling central Asian state in good shape.
Developed by QTS, the remote-controlled robots straddle the rails on treads. They can be used for tasks such as transposing tracks so the side of the rail that gets worn by the wheels of trains is switched to the outside.
The firm is in the early stage of talks which are being facilitated by the honorary consul for Mongolia in Scotland, David Scott.
South Lanarkshire-based QTS also hopes to win business in Australia.
Owned by Alan McLeish, a qualified tree surgeon, the company plans to move into exports to help maintain the rapid growth rates it has achieved in recent years.
In the year to March, QTS increased profits before tax by almost 50%, to £2 million, compared with £1.4m in the preceding year.
Sales surged 75%, to £24m, from £13.8m.
Started by Mr McLeish in 1991 with a £300 loan that he used to buy a chainsaw, QTS has become a big player in the rail maintenance market.
In the latest year the company won a series of contracts to work on projects for Network Rail across Scotland.
The workload included the design and construction of a new station building at Dalmuir, Clydebank; fitting major rock-fall netting near the railway line at Lunan Bay in Angus; and fencing work on the West Coast Main Line.
The company has been extending its reach south of the Border, and is currently working on a rail project in Kent.
The company's expertise in areas such as removing vegetation from structures is also in demand from the likes of BT and local authorities.
Based on current trends, directors expect the company to achieve further growth in the current year.
Mr McLeish said: "These results allow us to really build for the future, whether that is with overseas work, developing our workforce or investing in green energy at our HQ.
"Crucially these results allow us to reinvest profit in our Road Rail Vehicle research, development and production which will help keep us ahead of our competition in railway operations."
The company has doubled staff numbers to 81 in the past two years.
It expects to invest more than £1m in upgrading its vehicle fleet, plant and machinery in the current year.
The QTS group is the shirt sponsor of Kilmarnock football club for the 2012/13 season.
After leaving school with no qualifications, Mr McLeish built a career in forestry out of seasonal work in the sector before he started working on rail-maintenance projects.
Mongolia opened a consulate in Edinburgh in April as part of a drive to encourage Scottish companies to help the state maintain its rapid economic growth.
The country recorded growth of 17.3% in 2011 on the back of demand for commodities.