Direct Edge is the fourth-biggest U.S. market operator, handling almost 10 per cent of the daily trading in American stocks.
Its owners include Wall Street investment banking giant Goldman Sachs.
The Journal did not name its sources.
The TMX Group said it would not comment.
TMX, the operator of the Toronto Stock Exchange, is itself in the sights of a consortium of banks, The Maple Group, as an acquisition target.
And late Wednesday, the B.C. Securities Commission and Alberta Securities Commission signed off on the Maple Group's takeover bid.
Both the federal Competition Bureau and the Ontario Securities Commission gave their approvals earlier.
The Journal said negotiations between TMX and Direct Edge won't be concluded, if at all, until the deal with the Maple Group is made final.