Thiago Alcantara "would love Liverpool", according to former Bayern Munich captain Lothar Matthaus, who insists the midfielder would "fit perfectly with Jurgen Klopp".
Bayern snapped up Thiago from Barcelona for €25 million (£23m/$28m) in the summer of 2013, and he has since become one of the most important members of their squad.
The 29-year-old has racked up 231 appearances for the German champions in total, scoring 31 goals while also laying on 37 assists.
Bayern have won 15 trophies with the Spain international pulling the strings in the middle of the park, including seven Bundesliga titles, the latest of which was secured last month.
However, Thiago only has one year left to run on his current contract at Allianz Arena, and has yet to reach an agreement with the club over an extension.
Hansi Flick is hoping that the former Barca star chooses to stay put, but the Bayern boss has conceded that it would be "normal" for the playmaker to seek a new challenge in a different league as he heads into the latter stages of his career.
Anfield has been mooted as a possible next destination for Thiago, with Liverpool reportedly lining up a summer swoop for his signature.
Ex-Bayern and Germany midfielder Matthaus thinks the Spaniard has all the attributes to slot into Klopp's line-up seamlessly, and cannot see him remaining in Bavaria for another season.
“With Thiago, I’m pretty sure the signs are goodbye,” the 59-year-old told Sport Buzzer. “What other reason would he have for not yet accepting Bayern’s offer?
"Liverpool are obviously very keen on him and he would absolutely love the football, the team and fit perfectly with Jurgen Klopp."
Bayern CEO Karl-Heinz Rummenigge also weighed in on Thiago's future over the weekend, telling Bild: “We had serious negotiations with him and fulfilled all of his wishes.
"But it looks like he might want to do something new again at the end of his career.
“We don’t want to lose a player for free next year. I say that very clearly.”
Thiago featured in 29 domestic games for Bayern this season as they secured a league and cup double, and could add to his impressive silverware haul if Flick's side can conquer Europe when the Champions League resumes in August.