The Reds, who have been crowned champions of England a record 18 times, last won the top-flight crown in the 1989/90 campaign.
While Rafa Benitez's side have drawn far too many games for their liking this season, the 2-0 win over Chelsea on Sunday sees them just two points behind pacesetters Manchester United.
Former Real Sociedad midfielder Alonso, who has been at Anfield since the summer of 2004, believes Liverpool can pip Sir Alex Ferguson's troops and become Premier League champions for the first time.
"I am sure this is the best chance we'll have of winning the league since I arrived," explained Alonso.
"When I first came to the club I saw what the project was and now it's finally beginning to happen.
"At the moment it's looking good and we know Manchester United are the team we need to catch."