The National League club have been looking for their next boss since John Still resigned on May 17.
He took over at Barnet the next day and the club have since been forced to release a number of senior players.
The Daggers still face off-field battles but they expect to be in a position to announce their next manager by the middle of next week.
A statement has been released reassuring fans that focus is on next season.
“The club’s board, together with the representative from the Full Members Club, Mark Odams, met on Tuesday evening to short list the applications received,” it read.
“From over 85 applications a short list of seven has been drawn up and the interview process has already begun.
“This will continue over the weekend and into Monday.
“Obviously supporters will appreciate that it would not be appropriate to list the names of those who have applied but it is anticipated that an announcement for the new manager can be made by Wednesday.”