Managing partner Graeme Finnie admitted French Duncan was looking at expansion in the east and north of Scotland.
A move into the north of England is also part of the long-term growth plan and has been considered at board level.
The accountancy profession has not seen the same pace of mergers as in the legal sector but notable deals in recent months include Johnston Carmichael and Ritson Smith and the agreement between BDO and PKF.
Mr Finnie said finding the right merger deal was difficult and admitted French Duncan had turned down "several" approaches in the past year.
He said: "There is a huge opportunity for indigenous practices in Scotland and we are very ambitious to grow.
"We want to consolidate our position but are still on the hunt for the right merger.
"We have had a couple of approaches which we have turned down because they were not the right fit for us.
"For example, with Macfarlane Gray we courted them for the thick end of the year and thus far, a few months in, it is a real instance of two and two equalling five. So we would like to strengthen our offering in the east of Scotland. After that the most obvious route is north, and being frank we have had thoughts that Carlisle is somewhere we would like to go to.
"Some of our competitors have moved into London but that is not something we would do in the short term, but the ambition is to be substantial."
Mr Finnie said the existing Edinburgh office, created through a merger with McCabes in 2007, is responsible for about 15% of the firm's £10 million turnover and houses about 40 staff.
He said: "We are not weak in Edinburgh but we think there is an opportunity to grow in [that] market."
The firm also announced Paula Galloway has joined as an audit partner from KPMG, where she had spent more than two decades.
Ms Galloway – who has experience of working internationally having spent time in Hong Kong – becomes the ninth senior person to come from a Big Four accountancy practice to French Duncan in the past two years.
Mr Finnie, 43, said he believes the firm has invested around £1m in new directors and partners over that period.
He said: "We have found people in their 30s through to late 40s and early 50s are perhaps looking for more of a work- life balance [than they get at the Big Four].
"We remunerate them well but I like to think they get a lot of job satisfaction.
"They are not out for three months at a time on one audit. They are genuinely out and about as a business adviser with clients coming to them with various problems."