The 20-year-old has impressed for the Saints in recent weeks, starting and scoring in successive Premier League matches against Wolverhampton Wanderers and Burnley.
According to Goal, Chelsea inserted a recall clause into the temporary deal which saw Broja join Southampton this summer, and the Blues are now considering whether they should activate it in the winter window.
The German boss is now contemplating the idea of integrating Broja into the first team, to bolster his squad and provide competition for both Lukaku and Werner when they are fully fit.
Saints head coach Ralph Hasenhuttl is keen to keep hold of the striker for the remainder of this season, but he may have to enter the January transfer market to find a replacement, if the youngster returns to Stamford Bridge early.
Broja scored three goals in as many games for Chelsea during pre-season, after netting 11 times in 34 appearances across all competitions for Dutch side Vitesse in the 2020-21 campaign. body check tags ::