The on-loan Leeds left-back sustained a hamstring injury in last weekend`s 3-2 win over Peterborough and is now facing a lengthy spell in the treatment room.
Bessone is one of three players currently on loan at The Valley and Powell is keen to bolster his squad.
"It`s something we`ve been trying to do," he told Charlton`s official website. "We`ve made a few phone calls because I still fell we need to add to the squad.
"Sometimes you lose out to Championship clubs when players have that option. It`s an ongoing process for us and we`ll endeavour to get the right players to join us."