The Blues are serious about a move for the 28-year-old as they look to bolster their defensive options for next season.
BILD says the club have scheduled contract talks with Alaba's agent Zahavi in January.
Coincidentally, Zahavi is a close friend of Chelsea owner Abramovich and the Israeli helped engineer his take-over in west London in 2003.
He also played an integral role in the influx of players that arrived at Stamford Bridge to kickstart the Abramovich era.
Zahavi has maintained a close relationship with Abramovich ever since and the pair could work together again to bring Alaba to Chelsea next year.