The pair played in internal matches over the international break, having stepped up their training programmes in the last few weeks.
However neither appeared in the televised warm-up for Friday’s session ahead of facing Bournemouth, with Romeo Lavia also absent.
Broja has been out since December with knee ligament damage, while Badiashile was sidelined with a hamstring injury sustained in May.
Chelsea have taken an ultra-cautious approach over their returns and will likely wait until Aston Villa’s visit to Stamford Bridge next week before playing them. It means they will miss out on Sunday’s trip to Bournemouth.
Chelsea have nine players currently out amid an ongoing injury crisis. The club ended last season with the worst injury record in the Premier League, losing players for a combined total of 1,836 days and 216 games throughout the season.
The medical staff are trying to improve their record, but they lost new signing Lavia to an ankle injury over the international break.
The 19-year-old, who joined from Southampton for £58million last month, will be out for more than a month. He joins Reece James, Christopher Nkunku, Wesley Fofana, Carney Chukwuemeka, Trevoh Chalobah and Marcus Bettinelli on the sidelines.