Defenders Abu Ogogo and Paul Rodgers and midfielder James Dunne are currently training with Forest with the view to landing deals.
"The Club has made the decision that they will let them go out and trial with other clubs," Banfield told Arsenal.com. "It is between us and the players and how we see their future.
"Nottingham Forest have said they will have a look at them for 10 days and let them play in their reserves, with a view maybe to offering them a contract. We try to help them every way we can.
"At the moment we don't know what the all-round situation is but they have been allowed to go up there to work with [Forest manager] Colin Calderwood.
"We like to look out for all our players at the Club and if it maybe isn’t going to happen for them here we try to get them a place at another club as soon as we can to help them on their way in their career."