Alaba is said to be considering his future at Bayern Munich amid links to top European clubs.
The 27-year-old won his eighth Bundesliga title with the Bavarian giants last season and, despite an earlier dip in form, they sit at the league's summit once again.
Bayern sit four points clear of their biggest rivals Borussia Dortmund at the top of Germany's elite division.
Chelsea are reported to have initiated interest during the January transfer window and could make a summer move for the player.
The Blues were apparently confident they could tempt Alaba into a move by offering him a new challenge in the Premier League.
Frank Lampard is keen to shore up the left side of his defence with it seeming more and more likely that Marcos Alonso is on his way out of the club.
However, according to Sport BILD (via BuliNews), La Liga heavyweights Barcelona and Real Madrid could pose serious competition for Alaba.
Alaba came through Bayern Munich's youth set-up and broke through to the first team after having spent 6 months on loan at Hoffenheim in the 2010/11 campaign.
The Austrian also holds the record for the youngest ever player to be capped by his country at just 17 years old.
Alaba is believed to be valued at around £60m which could rise if a bidding war were to break out between the interested parties.
Alaba has previously expressed his desire to play in Spain or England and even specified Real Madrid and Barcelona as preferable destinations.
"Spain, England [the countries he wants to play in]," he told BILD last year.
"In Spain, it would be the two big clubs, I guess, Real or Barcelona. Also the big clubs in England."
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