Citing sources close to the deal, the Journal reported that an announcement could come as early as Monday, provided the deal goes as planned. Alaska Air is expected to pay at least $2 billion for Virgin, the publication added. News of the deal was first reported last month by Bloomberg News.
A deal would immediately vault Alaska to the number 5 U.S. air carrier, a spot currently occupied by JetBlue. Virgin America is majority owned by billionaire Richard Branson's Virgin Group Ltd. and New York-based Cyrus Capital Partners LP.
Representatives for Virgin and Alaska Air did not immediately respond to CNBC's request for comment.
The full report can be found on the WSJ's website.