Messi's superb treble against Atletico Madrid, the 24-year-old's 11th career hat-trick, put him on 192 goals, two behind Hungarian Kubala, who played for Barca in the 1950s and early 1960s. Cesar Rodriguez is the club's record marksman with 235.
"I just take it a game at a time but obviously I'm very excited," World Player of the Year Messi told Barca TV on Sunday.
"Hopefully I can overtake him [Kubala]," he added. "I want to continue making history here."
Messi made his debut for Barca's first team in October 2004 and became the club's youngest league scorer when he netted against Albacete in May 2005 at the age of 17 years, 10 months and seven days.
In five La Liga games this season, he has already scored eight goals, one more than last term's top scorer Cristiano Ronaldo of Real Madrid.
"Messi was decisive again, you can only congratulate him," Barca coach Pep Guardiola said after Saturday's 5-0 victory over Atletico.
"He's a player that you don't have to explain, you just have to watch him in action.
"He is two goals away from Kubala's record, at 24 years old. It's all been said, there's not much to add."
Messi, typically, argues that his success comes from playing in a great team and says individual awards are secondary.
"I think the most important thing for this team is to keep winning, and keep winning titles for us and the fans," he told Barca TV.
"This is far more important than any individual prize or statistic."
