The £2.5m project aims to form a "catalyst" for further development of the area and help Leeds become a more child-friendly city, said the local authority, which has put up the money and drawn up the plans.
Sovereign Street car park will be transformed into a landscaped area with paths, seating and mounded earth forms. It will form a spill-out area for office workers to a new development. A more detailed cost report is being drawn up and a consultation is planned.
"The new public area fits our ambition to extend the city centre southwards and address its shortage of good-quality green spaces," said councillor and executive member for development Richard Lewis.
"When times are hard and the economy is facing big challenges new development tends to stagnate. But in Leeds we are not accepting that. We are taking action to do everything we can to stimulate growth in the city.
"And it’s not all about attracting new investment; we want to make sure our city has the best infrastructure for its people by protecting and providing precious green spaces. Our plans for Sovereign Street will help us achieve all those aims."