Citing a person familiar with the matter, the publication said discussions are still at a sensitive stage and could well break off.
A spokeswoman for YouTube could not be reached for comment and Google declined to comment on "rumors and speculation."
According to the report, YouTube commanded 46 percent of visits to U.S. online video sites in August, compared to a 23 percent share for the video activities of MySpace and 10 percent for Google Video.
YouTube says consumers view videos over 100 million times daily through its service and upload more than 65,000 videos each day.
"YouTube has stood out from the growing crop of online video services for its simplicity," the Journal reported. "[It] serves up videos that generally can be viewed without users downloading special software. It also let consumers display its videos on other sites, such as blogs or personal pages on MySpace."
A YouTube buyout would represent one of the largest acquisitions for Google, the report adds. Although it sits on nearly $10 billion in cash, the Mountain View, Calif.-based company has focused mostly on smaller targets such as Pyra Labs, the company behind the Blogger service, online photo-search firm Picasa and satellite-mapping company Keyhole.
Last month, it was reported that Google and Apple had entered into discussion about making files from Google Video easily accessible by the new Apple $299 iTV device, due out early next year. Therefore, a YouTube acquisition by Google could possibly broaden the magnitude of content available to iTV adopters.