At time of writing, the the Korean pop mega hit had accumulated almost 795 million views since it was posted on 15 July this year. Baby, which has been available since February 2010, had 803 million views.
With Gangnam Style attracting about 11 million views per day compared to Bieber's one million, it is due to take the crown this weekend.
The song, which pokes fun at the fashion-conscious denizens of a wealthy district of Seoul, has powered its singer, Psy, to global stardom. An array of public figures including the sculptor Anish Kapoor, Zara Phillips and Ban Ki Moon have copied his "horse riding" dance.
In October Gangnam Style also became the first Korean song to top the official UK pop chart.
Jespite their YouTube rivalry, since achieving stardom in the West, Psy has reportedly signed up with Justin Bieber's management company and said the pair will work on a song together.