The Edinburgh company says the approach may result in it entering international markets earlier than anticipated.
It had previously planned to look at growth outside the UK in 2014.
Now managing director Brian Williamson is expected to fly to Australia for further discussions.
While he would not reveal the name of the interested party, Mr Williamson said Jumpstart had identified more than 40 other countries with similar tax redemption policies to the UK and believes the firm's business model is scalable.
He said: "There are many countries in the world with R&D tax credit schemes which are similar to Britain's, but it is very desirable to make our first move in a country such as Australia where the market is not highly developed and where there are language and cultural resonances.
"Successful growth in Australia would provide for us a valuable template which we could then transplant to tax jurisdictions even in countries where English is not the first language.
"Governments around the world, in recognition of the international nature of competition, have made funds available to foster and encourage innovation and research. It is part of our global strategy to make sure that these resources can be efficiently tapped."
Jumpstart employs engineers, scientists and software specialists among its 100-strong team and they help companies identify what tax benefits they may be eligible for.
The company, founded in 2008, has a conservative expectation that turnover should reach at least £3.5m next year based on the current order book.