The 25-year-old defender has been linked with a number of big European clubs in the recent years having garnered a reputation as one of the best left-backs around Europe.
In March 2016, Mundo Deportivo reported that Barcelona had identified Alaba as a "dream signing" with the Catalans seeing him as new Eric Abidal, with the ability to adapt to both the heart of the back-line and the left-back role.
Days later the Austria international appeared to close the door to such a move by agreeing to commit his long-term future to Bayern until 2021.
However, AS reported in January 2017 that Barcelona plan to reignite their interest in the upcoming summer transfer window after having earmarked him, Atletico Madrid ace Antoine Griezmann and Gremio starlet Arthur Melo as the three priorities for the 2018-2019 campaign.
Valverde already has Jordi Alba and Lucas Digne to cover the left-back role but AS says that the Catalans could are considering partying ways with the former Frenchman to make space for the Bayern star.
Nevertheless, the France international has failed to make the impact expected at the Nou Camp since his arrival from Paris Saint-Germain in the summer and his future at the club came under question in the summer when Ernesto Valverde's side battled with Real Madrid for the signing of Theo Hernandez [Sport] from Atletico Madrid.
AS add that Barcelona also value his versatility and Alaba himself has now put the Catalans and other potential suitors on alert after suggesting that he could consider moving away from Bayern in the future.
"I am aware that this decision will come to me. I still feel very comfortable here, but I can also imagine taking a different path, taking the next step or looking for a new challenge. But I leave that decision open. I have goals for this season that I want to achieve, so there's no room for that right now," Alaba said during an interview with Austrian outlet Kurier.
"I am at an age where I have had a lot of experience and where I would like to take the next step in my career. It is also part of taking the next step in Bayern, of growing into a leadership role, assuming responsibility and passing on my experience, especially for young players who follow suit. I think that the club expects me to slip into a leadership role."