State attorneys general are discussing launching their own antitrust probe of big technology firms such as Facebook (FB - Get Report) and Alphabet's (GOOGL - Get Report) Google unit, according to a published report Monday.

The formal effort could get underway as early as September, The Wall Street Journal reported, citing unnamed sources.

Earlier this summer, the Department of Justice launched its own review of antitrust issues surrounding tech companies. The Federal Trade Commission is also investigating Facebook.

Alphabet shares rose $21.23, or 1.8%, to $1,200.44 Monday. Facebook shares rose $2.47, or 1.34%, to $186.17. 

Separately, FTC Chairman Joseph Simons told the Financial Times that breaking up Facebook would difficult to do, especially if the company ties together its three major platforms: WhatsApp, Instagram and its traditional newsfeed.

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