The 28-year-old is set to leave the Allianz Arena when his contract expires in June.
The Austria international has confirmed that he would end his 13-year association with the Bavarians to pursue a fresh challenge elsewhere.
Liverpool and Manchester City have been linked with the centre-back in the past but 90min suggests that Chelsea are the only English club to contact him.
The Blues are prepared to offer him wages of more than £300,000-a-week.
Alaba has his sights on signing for Real Madrid and talks are in an advanced stage with the La Liga champions.