Councillor Jim O’Boyle said: “This is a unique opportunity to create something very special, not just for the city and the region, but for the country’s wildlife.
“We know the UK is one of the most nature depleted nations in the world, with one in six species at risk of extinction, and everyone has to take action.
“We made a commitment in the council’s Climate Change Strategy to do all we can to support nature recovery - and this site presents a significant opportunity to do that at a scale rarely seen.”
The council would need to obtain planning permission for the change of use from Rugby Borough Council and would then work with Warwickshire County Council and other partners to develop the site.
That includes Warwickshire Wildlife Trust, which manages land around the golf course and has its headquarters at the neighbouring Brandon Marsh Nature Reserve.
Mr O’Byle said there was also the possibility of building an outdoor education centre on the site of the old clubhouse.