^^ Nope (well atleast not from these specs)
2013 Subaru BRZ Price Starts at $24,000 - And We Have the Detailed Specs! - WOT on Motor Trend
Also, for those wondering about the block being the same as the previous generation EJ, NOPE!!
So the idea behind swapping in just the STI heads just became that much more difficult..........
I am going to go out on a limb here and say that the mounting points, etc, might be that much more different to cause a few headaches as well...........
2013 Subaru BRZ Prototype First Drive - Motor Trend
The key to the BRZ's appeal is the unique hardware under its relatively conventional skin. This is the world's only front-engine, rear-drive sports car powered by a boxer engine. The Subaru 2.0-liter four is an all-new engine with a different block from that used in the 2012 Impreza, and features Toyota-sourced direct injection. It gets a unique FA designation within the Subaru engine family (the closely related 2012 Impreza engine is known as the FB, while the 2011 Impreza is the EJ), and though Subaru engineers were tight-lipped about the engine's output, they didn't disagree with our guess of about 200 hp and 170 lb-ft. The engine drives the rear wheels through a choice of two Aisin six-speed transmissions, one a manual, the other a conventional planetary automatic with manual actuation via steering wheel-mounted paddles. The transmission is the same one used in the Lexus IS 350, among others. Front suspension is MacPherson strut, while the rear gets a complex multilink setup. Brakes are disc all around.