Both players are nearing returns from injury which will boost Dean Smith’s options as Villa look to halt their slide down the Premier League table.
England international defender Mings has not featured since suffering a hamstring injury early in the 4-1 defeat to Leicester on December 8.
Striker Davis, meanwhile, has been out for two months with a hamstring injury sustained in Villa’s Carabao Cup victory over Wolves in late October.
Villa are likely to be without Matt Targett for the trip to Turf Moor after the left-back suffered a hamstring injury of his own in Saturday’s 3-0 defeat at Watford.
Neil Taylor could make his first Premier League start since September’s 3-2 defeat at Arsenal. Targett’s injury prompted Smith to question a festive schedule which saw many Premier League teams play twice in the space of 48 hours.
“There was always going to be a chance someone would get injured, due to somebody’s idea of playing two games in three days,” said the boss.
“They expect players to be professional athletes and then put them through what they have over the last couple of days.”
Villa head to Burnley desperate for a positive performance and result, following a run of five defeats in six league matches which sees them end 2019 in the relegation zone.
Smith questioned the commitment of his players in the wake of the weekend’s drab showing against the Hornets.
“I’m looking for the players to stand up and be counted – myself included,” he said.
“Go and win tackles, go and win headers, go and compete, show work rate. That’s what you need to go and win games.”