Defender Williams and forward Cotterill are both on international duty with Wales and will be preparing for the national team’s friendly against Luxembourg on Wednesday.
Swans manager Brendan Rodgers, who is taking charge of his first competitive game at the Liberty Stadium, will also be without five players on duty with Wales’ Under-21 squad in Malta – David Cornell, Jazz Richards, Daniel Alfei, Neil Taylor and Shaun MacDonald.
Midfielder Joe Allen has been out of action since the end of last season after undergoing surgery but was given the green light to resume full training on Saturday and could be in contention to line up against the Bees.
In-demand right-back Angel Rangel is unlikely to be risked so soon after pulling out in the warm-up shortly before Saturday’s 2-0 defeat at Hull due to a niggling thigh injury.
Midfielders Ferrie Bodde (knee) and Tom Butler (thigh) and striker Craig Beattie (calf) also remain on the sidelines.