The Lions are looking for a replacement for Kenny Jackett after he resigned at the end of the season after almost six years in charge.
Burnley boss Sean Dyche, former Bolton chief Owen Coyle and QPR youth coach Marc Bircham are among the names being linked with the job.
Berylson told the club website: "The board has been impressed by the quality of applicants for the manager's position here, and our aim is to review them all by the start of next week and draw up a shortlist.
"I would hope that we will then begin the process of interviewing later in the week, taking as long as is necessary until we are clear that we have the right man for the job.
"We are fortunate to be going through this process early in the closed season because we are not under undue pressure.
"However, we are mindful of the fact that the new manager will need as much time as possible to organise his pre-season and start to re-structure the squad as he sees fit.
"It goes without saying that this appointment will be a massively important one for us. We got it right when we appointed Kenny Jackett five-and-a-half years ago. "