Defender Dickson, 25, and striker Forte, 26, spent much of last season on loan at Leyton Orient and Notts County respectively.
Barnard joined on a free transfer from Southend in 2010 but the 28-year-old striker has been deemed surplus to requirements.
"It's fair to say that (they can leave)," Adkins told BBC Radio Solent.
"There has been interest in them because they are of good quality.
"They are fit but they need to play football as well so everyone is working very hard to create a win, win situation.
"I'd imagine as the month progresses something more concrete will materialise."