Controversy over the future of a key asset owned by the Sydney Harbour Federation Trust is set to intensify, with a private philanthropy group unveiling a bid to lease and "re-imagine" the whole of heritage-listed Cockatoo Island for at least 50 years.

The Cockatoo Island Foundation Limited wants to transform the prize Commonwealth-owned site into a "permanent art island for Sydney", complete with major art installations, permanent and temporary art exhibitions, "immersive" visitor experiences, food and beverage offerings and other unspecified "potential uses".

Cockatoo Island is one of the sites that belongs to the Sydney Harbour Federation Trust.

The foundation says a new body, not the trust, should manage the site, because the island has been "severely underused" and is a "missed opportunity for Sydney and Australia".

"Our observation is that there is no clear vision for the future of the island, and no clear sense of what its owners and stakeholders want the island to be" it says, in its submission to a review commissioned by federal Environment Minister Sussan Ley.