Basham has enjoyed a new lease of life at Bloomfield Road since Appleton succeeded Ian Holloway as manager, starting five times and impressing in the holding midfield role.
The 24-year-old's ankle problem ruled him out of Saturday's 2-0 victory over Blackburn but Appleton is confident Basham will be back at his disposal for the festive period.
"We're hoping it's short-term," he told BBC Radio Lancashire. "Whether he'll be ready for Wolves on Friday, we're not too sure.
"He's got a tear in his ligament, but it's not a substantial one that you would expect to keep him out of action for weeks and weeks."