The popular midfielder returned to the Liberty Stadium on Thursday, signing a two-and-a-half year contract for an undisclosed fee, having failed to settle at Sheffield United after ending an eight-year spell in south Wales in the summer.
Manager Brendan Rodgers must now decide how to use Britton, with a wealth of midfield talent already at his disposal in Darren Pratley, Mark Gower, Joe Allen and Kemy Agustien.
Fellow midfielder Andrea Orlandi (thigh) has returned to training this week and could also feature in some capacity at Oakwell.
But left-back Neil Taylor (ankle) remains up to three weeks away from a first-team return although he should be back training again next week.
And with captain Garry Monk (knee) a long-term absentee, that means Rodgers is likely to stick with the same defensive quartet who kept a clean sheet against Crystal Palace last weekend - Alan Tate, Ashley Williams, Angel Rangel and Ashley Richards.