Ajax expect to keep hold of youth coach Dennis Bergkamp next season.
Bergkamp is a target for Arsenal.
The Mirror says technical director Marc Overmars, another former Gunner, is hoping to keep him at the Amsterdam club for one more year. That would suit Arsenal, who need Brady's replacement in place by May 2014.
"Getting Dennis to sign a new deal is our first priority,'' said Overmars.
Moving back to London would be no problem for Bergkamp as his children were born and brought up in England and attended schools in London.