The Reds hierarchy are currently searching for the man to step into the shoes of Jurgen Klopp, who announced last month that he would be stepping down from his Anfield post at the end of the season.
Two months on from informing the owners of his decision to resign, Klopp told supporters that he was "running out of energy" to continue as Liverpool head coach any longer, despite possessing a contract until 2026.
Work is already underway to identify the best candidate to replace the Premier League and Champions League winner, and Alonso has been the firm favourite to take the reins ever since Klopp's bombshell revelation.
The former Reds midfielder - part of their 2004-05 Champions League-winning squad - has masterminded a magnificent start to the Bundesliga season with Bayer Leverkusen, and the German top-flight title is currently theirs to lose.
With 52 points from their opening 20 fixtures, Leverkusen sit two points clear of perennial champions Bayern Munich - who have won the last 11 editions of the Bundesliga - at the top of the mid-season standings.
While Leverkusen's 52 goals scored is fewer than that of Bayern (59), Alonso's men have been the stingiest defensive unit in the league, only letting in 14 goals throughout the entire campaign so far.
The 42-year-old's deal with Leverkusen also runs until the summer of 2026, and the German side are believed to be confident of retaining his services despite interest from the Reds, as well as former clubs Bayern and Real Madrid.
It has been reported that Liverpool have already made contact with Alonso to gauge his interest in the job, although they will refrain from accelerating their pursuit while Leverkusen are challenging for title glory.
However, Schweinsteiger - as quoted by the Daily Mail - claims that Alonso will indeed depart Leverkusen at the end of the current campaign, and the Spaniard is eyeing the top job at Anfield.
"I know him, and I am sure his dream is to coach Liverpool. I am sure he will leave Leverkusen in the summer," Schweinsteiger said while working as a pundit in Germany.
Since being appointed Leverkusen boss in October 2022, Alonso's side have claimed 43 wins, 14 draws and 10 defeats from his 67 matches in charge, and Die Werkself reached the semi-finals of the Europa League during his first season in charge.
With Real and Bayern potentially also making a play for Alonso, though, Liverpool are running the rule over other candidates, including Sporting Lisbon head coach Ruben Amorim.
The likes of Zinedine Zidane, Thomas Frank, Roberto De Zerbi and Julian Nagelsmann have also been linked with the role, and the latter - currently in charge of Germany - recently admitted that he does not know what the future holds after Euro 2024.