The 28-year-old is expected to leave Bayern on a free transfer when his contract runs out next summer but he is free to negotiate with overseas clubs directly from Jan. 1.
Sources have told ESPN that Chelsea have asked to be kept informed of the situation as head coach Frank Lampard looks to strengthen his defensive options.
Lampard also confirmed the club have an option to extend veteran centre-back Thiago Silva's one-year deal by a further season but Alaba has emerged as an intriguing option to further boost his squad depth.
Alaba is best known as a left-back but can play at centre-back or in midfield, providing useful flexibility to cover in a number of positions.
Lampard has publicly acknowledged the size of his squad will need to be trimmed in future windows so any pursuit of Alaba may also depend on outgoings.
Ben Chilwell has made an impressive start at the club following his £50 million arrival from Leicester City but Lampard is expected to make fellow left-backs Emerson Palmieri and Marcos Alonso available for transfer either next month or at the end of the season.
They believe Tomori has a long-term future at the club but are keen to loan him out to gain more first-team experience, while Rudiger was determined to fight for his place yet has started just four games all season.
Alaba would command a wage at the top end of Chelsea's current pay structure -- in excess of £175,000-a-week -- but the absence of a transfer fee makes him a cheaper alternative to Rice, with West Ham valuing the England international at £80m earlier in the year.