The 28-year-old defender will be out of contract in the summer and has already been linked with a move to a number of Europe's top clubs on a free transfer at the end of the current season.
According to Bild reporter Christian Falk [via Metro], the Austrian defender's representative Pini Zahavi is set to begin talks with Chelsea in January over a potential move to north London for Alaba in the summer transfer window.
However, the Blues are likely to face competition from Paris Saint-Germain, who are also said to be interested in the Bayern defender. He's also been linked with a move to several other European clubs, including Manchester City and Liverpool.
Meanwhile, Chelsea bolstered their defence in the recent summer transfer window, as they signed Thiago Silva and Ben Chilwell, both of whom have had an impressive start at the club. If they manage to lure Alaba as well to north London next summer, it could further reinforce the Blues' defence, which has leaked in just 10 goals in the English top-flight so far this season.