The foundation is in the process of appointing a new architect in the UK after previously employing one based in Italy.
The latter completed several designs which were sent to Reading Council, the community and Historic England for approval.
But feedback suggested they did not convey the cultural and historical significance of the site, some of which is Grade II listed, and the foundation expects to confirm the appointment of the UK-based architect soon.
After Wilde was released in May 1897, he spent the last three years of his life in exile in France, where he composed his final work, The Ballad of Reading Gaol, describing an execution at the prison.
Previous plans for the site included Thames Valley Police using part of it as a training ground for armed police.