It has been nominated by Highland Council, and now aims to be one of 20 set up throughout Scotland under the first phase of an initiative which is intended to transform schools that produce sustainable plans to energise their performance.
Successful candidates will receive pound;100,000 a year for three years to turn themselves into what the Executive describes as "flagships of innovation, leadership, ambition and opportunity".
Bruce Robertson, Highland's director of education, said: "This is about schools that want to change the way they deliver education. The high school fits the criteria very well because it is already putting many good ideas into practice. Pupils themselves have been at the heart of changes.
"The school received a critical report from inspectors two years ago, but there have been a lot of improvements since then. The schools of ambition project is about offering more vocational opportunities for young people and involving the local community in setting the direction and the running of the school.
"Standards are raised and a set of improvements will take place in the curriculum. It also increases the capacity of the staff, which will boost the staff themselves."
Inverness High has been running a project known as Real - "real education active lives". It has a strong focus on stimulating success in its local community - to "grow social capital and social enterprise", as it puts it.
There is also an emphasis on vocational education, improving leadership and enhancing ICT.
The action taken by the school in response to a critical HMIE report has so impressed the district inspectorate that it now regards progress there as a model of good practice.
Mr Robertson made clear in his report to Highland's education committee last week that Inverness High would not be the only beneficiary of the bid.
"Schools across Highland will be able to benefit from a successful bid on behalf of Inverness High. We will build into the specification of the project the need to disseminate good practice, create opportunities for staff from other schools to share in development activities and shape our thinking for further bids into the programme," Mr Robertson said.