Loosemore abruptly resigned last month and officially left the under-pressure PLC on 1 May.
In its update, De La Rue said: “Interviews have taken place with a range of candidates who have come forward with the support of shareholders and partners, as well as from search activities.
“We are not yet at the stage of making a final appointment but are progressing candidates through the final stage of our process. These candidates have strong backgrounds in relevant situations.”
Bray has been a non-executive director at the security printing and authentication business since 2016, and is the CFO at tech firm Travelport.
Activist investor Crystal Amber Fund called for Loosemore to be replaced in March, and has already put forward private equity expert Pepyn Dinandt to be the new chair.
De La Rue previously said that Dinandt would be considered for the role as part of the fast-track process.
The group also has an interim CFO, Charles Andrews, with incumbent Rob Harding set to step down over the summer when he completes his six month notice period.