That's the claim of the Mail on Sunday who report that the Liverpool boss would love to sign the Real Madrid star after missing out on top midfield target Henrikh Mkhitaryan, who is joining Borussia Dortmund from Shakhtar Donetsk.
Alonso would cost around £10 million, but the problem is not the fee - rather, it is Alonso's age.
At 31, he would have little sell-on value in the future which goes against the 'Moneyball' principals of owner John Henry, who is reluctant to invest in players in the latter stages of their careers.
Liverpool have already signed 32-year-old Kolo Toure, but that transfer was allowed to pass as the Ivory Coast international was available on a free transfer after his contract at Manchester City expired.
Alonso signed for Liverpool from Real Sociedad for £10.7m in 2004 and went on to play over 200 games for the club before being sold to Real Madrid for £30m in 2009.
To other rumours now, and Tottenham are hoping to continue their summer rebuilding by landing Aston Villa striker Christian Benteke.
They have a plan on how best to snatch the Belgian international too. The Sun reports that they are willing to wait until the end of the transfer window before making a £20m move rather than splash out the £30m that Villa are demanding at the moment.
Meanwhile, The Observer reports that Thiago Alcântara has a "good chance" of signing for Manchester United from Barcelona this week for about £17m on a five-year deal.
Thiago will receive "much-improved terms on his current £30,000-a-week contract" if he joins United, while also receiving guarantees on more playing time that he has been getting at the Camp Nou.
Rumours continue to swirl around some of the Premier League's top strikers too. The Sunday Mirror claims that Chelsea and Arsenal remain convinced Wayne Rooney can be prised out of Old Trafford this summer, despite new manager David Moyes insisting the striker will not be sold.
The paper says that the same two clubs have also made enquiries to find out whether Liverpool’s wantaway star Luis Suarez would consider moving within the Premier League.
Jermain Defoe is a target for new Stoke boss Mark Hughes – who wants to reunite the England striker with Peter Crouch. Tottenham are seeking a buyer for the £6 million-rated forward. (Sunday People)
Alvaro Negredo is expected to complete his £20 million move to Manchester City this week. The 27-year-old Sevilla striker was on the verge of joining Atletico Madrid, but the prospect of playing for Manuel Pellegrini at City is said to have convinced Negredo to make the switch to the Premier League. (Mail on Sunday)
Nick Powell is a loan target for Norwich. The Manchester United midfielder, 19, played just six times last season after joining from Crewe. (The Sun)
Finally, Crystal Palace are set to throw Carlton Cole a Premier League lifeline. The former England striker, 29, a free agent after being edged out of West Ham, has had preliminary talks at Selhurst Park. (Sunday Express)
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- Xabi Alonso
- Real Madrid
- Premier League
- Manchester United
- Borussia Dortmund