The on-loan Leeds full-back returned to the starting line-up in Saturday's 3-2 home win over Peterborough following a hamstring injury but was stretchered off in the 63rd minute after aggravating the problem. West Ham loanee Matt Fry will come in if Bessone fails to make it.
Midfielder Scott Wagstaff is also a doubt after he was forced off at half-time against the Posh with a head injury and was taken straight to hospital but he should have recovered in time.
Wagstaff's replacement at the weekend was Pawel Abbott, who did not travel to Yeovil in the previous game, but performed well against the Posh having a significant hand in the Addicks' third goal and will be pushing for a starting place against the Pools.
On-loan Liverpool forward Nathan Eccleston made his first start for the club against Peterborough and should keep his place as Paul Benson (hamstring) will again miss out as will fellow striker Joe Anyinsah who is struggling with a knock.
Defenders Kelly Youga (knee) and Chris Solly (ankle) remain sidelined although the latter is back in full training.