The 27-year-old has already bagged five goals in the Primera Liga this term, taking his overall tally to 248, just three strikes off the pace of Telmo Zarra, who set the record while playing for Athletic Bilbao some 60 years ago.
Barca are next in action against Rayo Vallecano on Saturday, but when quizzed about the possibility of soon breaking the record, the ever-humble Messi preferred to play down the important of such a statistic.
"Right now I am not thinking about the record," he said. "Sure, it would be nice to be the record top scorer in one of the best leagues in the world.
"But the record will come when it comes."