"He told me he didn't speak English too well before our unveiling press conference," Garcia told BBC Sport of that first meeting with his fellow Spaniard, both of them having faced each other repeatedly in Spanish football before that day at Anfield.
"I answered the first question in Spanish, as we had a translator present, and he answered in perfect English and I thought: 'Why you little?!'"
Both went on to start in Liverpool's dramatic Champions League final win over AC Milan that same season and later played together for Spain, forming a friendship that has endured more than two decades.
Now chief executive of Johor Darul Ta'zim, Garcia will welcome his old friend to Malaysia on Sunday, when Chelsea's Asia tour concludes at JDT's 40,000-capacity Sultan Ibrahim Stadium. The fixture comes after Chelsea have faced elite European opposition including Tottenham, Juventus and AC Milan across Australia and Asia, and Garcia knows exactly how big a moment it represents for his club.
"Chelsea is the biggest test we will face this season," he said. "I'll be so happy to welcome them in Johor. The stadium is going to be packed. We can't wait to challenge ourselves against a top club, top players and it is great to face Alonso. I can assure you on Sunday we will compete."
He added, with evident warmth: "I wish him all the best [at Chelsea], but even though I love him, hopefully he ends up second to Liverpool next season."
JDT arrive in good form, having drawn with Rangers and Spanish second-division side Elche before beating Cartagena during a training camp in Alicante. The Malaysian champions have not lost a domestic match since 2021 and are currently on a world record-equalling 108-game unbeaten run, one they could extend when the domestic season resumes in August.
"Hopefully in the first game of the season we'll break one of the most incredible records in football, that is the domestic unbeaten run," Garcia said.
Success is also growing on the continental stage, with JDT reaching the quarter-finals of the AFC Champions League last season.
"The owner is the Crown Prince, His Royal Highness Ismail Tunku. He has taken the club on an amazing journey. Top-class stadium and training facilities that people will be talking about. We don't have a limit, and that motto of 'the sky is never the limit' is something that we repeat quite often in the dressing room."
Garcia, who splits his time between Spain and Malaysia, gained his UEFA Pro Licence and sporting director licence after retiring, and while he leaves coaching duties to compatriot Xisco Muñoz, his role extends into commercial activity and wider planning behind the scenes, with Spanish coaches placed throughout the club's backroom staff and academy.
"We want to increase the level of Malaysian football and have a fantastic academy. We brought Spanish coaches to the academy so we can get closer to the best, professional style of work," he said.
"Spain winning the World Cup shows you the value of having a coaching programme and a football philosophy that lasts 25-30 years. We got to the quarter-finals of the Asian Champions League and would like more Malaysian teams in the competition."
Garcia was frank about the scale of the challenge JDT faced during that run, up against clubs operating on vastly bigger budgets.
"The next step is to compete in the Asian Champions League and last year was our main introduction. We arrived there, and we kind of caught up with the situation. It was difficult against teams that got budgets that pass over $150m and we only have $15m, so it's quite a difference, a big gap between. But we want to contribute to the development of Malaysian football to reach the World Cup some day."