Business Growth Fund (BGF) expects to close two deals in Scotland by the end of March and is targeting up to £50 million of investment in the country this year.
It is understood the deal closest to completion is in the oil and gas sector.
So far BGF's Scottish team has invested £25m, including taking stakes in Edinburgh-based morphsuits maker AFG Media, Aberdeen oil and gas services company STATS Group and East Kilbride technology firm M Squared Lasers.
The Scottish arm also worked on a deal with Portsmouth oil and gas pipe supplier Magma Global.
The latest investment targets were announced as part of an aim to plough £200m into businesses across the UK in 2013.
BGF, which made its first investment in October 2011, provided £120m to companies across 2012.
Simon Munro, regional director for BGF's Scottish team, said: "There is an addressable market and clear demand for growth equity among the UK's small and medium- sized businesses.
"Whilst this is undoubtedly much needed progress, we are under no illusions; there is still a lot to be done – and this is our focus for 2013."
"Our own commissioned research indicates that there are in the region of 4000 British companies with more than ten employees, and a turnover of between £2.5m and £100m, that are growing at 10% or more year-on-year. Around 5% of these businesses are based in Scotland. We need to see these numbers increase.
"We remain very ambitious for the year ahead. We see the potential to invest up to £50m in our region this year. This is a real cause for confidence."
BGF provides long-term capital of between £2m and £10m in exchange for a minority equity stake in a company.
The £2.5 billion scheme was established by five banks, including Royal Bank of Scotland and Lloyds Banking Group, in response to claims lenders were not doing enough to support small and medium businesses