His career later led him to Real Madrid and then Bayern Munich, but the midfielder will be watching the latest meeting between the two historic clubs attentively on Sunday and hoping Jurgen Klopp can engineer a memorable win at Old Trafford.
"Nothing means more to the fans than beating Manchester United," Alonso told Fox Latin America.
"During my time at the club we didn't have much success at Old Trafford but a win there would not only mean everything to the fans, but give Liverpool the real belief they have what it takes to win the title this season."
Alonso also had warm words for Klopp, whom he believes has settled in effortlessly at one of England's most demanding clubs.
"I respect him [Klopp] a lot for the way he has embraced the Liverpool culture - from the start he seemed to understand just what the job meant," he explained.
"He understands the hunger the fans have, but also he conducts himself with style and dignity.
"The Premier League has never been more competitive - but I really think the glory days of Liverpool Football Club could be very close again."