Trade magazine MCV understands that both platform holders will present their new consoles at the Los Angeles expo in June.
The move will ensure both companies aren't far behind Nintendo, who will be finalising their release plans for the Wii U.
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Microsoft has recently told partners that a new console showing at E3 will take place, while Sony executives have ensured third-parties that it will not be left behind as other firms make their announcements.
Speaking about the story, MCV writer Ben Parfitt said: "Obviously we can't reveal our sources. But you have my personal word on this - the source is exemplary, 100% concrete, ultra high level."
He added: "Really, really wish I could name him/her/them/it but obviously cannot."
In November, it was rumoured that both a new Xbox and PlayStation 4 would be released in 2012.
A recent report indicated that Microsoft's next system is codenamed Loop.
Elsewhere, rumours surfaced that suggested a 2013 launch for Microsoft's next system, while another analyst predicted that neither company would have a new system before 2014.
Watch a video of Microsoft's latest dashboard refresh for Xbox 360 below: