OnLive believes that if Sony and MS were to integrate its Cloud service on PS3 and Xbox 360, they would "make great consoles".
The Californian firm made waves at E3 earlier this month by showing off its new controller, which connects to OnLive's servers via most modern TVs and tablets wirelessly. It demoed a range of games playing glitch-free on iPad, including Gearbox's Borderlands and Ubisoft's From Dust.
The tech has been officially backed by major software publishers such as Warner and EA. However, OnLive is yet to seal an affiliation with any traditional hardware manufacturer, locking it out of access to platform-exclusive content - and a big chunk of the modern gaming audience.
When we asked OnLive VP of Engineering Joe Bentley if the company could see its service working with Microsoft and Sony's systems in future - rather than just bypassing them - he said:
"Absolutely, they would make great consoles. Our controller is a hybrid between a PS3 controller and an Xbox controller. It's all compatible, it would just work. There are OnLive guys chatting [Sony and MS], but we'll see where it goes. But it would absolutely work, we're ready to work with everybody.
He added: "What people are realising and waking up to is everything could be a console, why shouldn't you be able to take your game everywhere. I think the timing of this is perfect. When I joined the company I didn't think it was going to pan out this way.
"I give lectures at university and I tell people that finally the internet has grown to be fast enough, and that it's really the age of the SOC; the System-On Chips that you find in the iPad, the snapdragon. They're making these magical smartphones and tablets take off in a huge way.
"It makes you use your imagination: what would you do with faster Internet and these SOCs in TVs? It will soon be in everything up to refrigerators. This is what we came up with - turning everything into a console, not taking compromised gaming like Zynga or whatever but fully-fledged gaming with you.
"It has to be instant, because the reality is we have a very short amount of time. The reason mobile gaming has taken off is because you can occupy your time at the bus stop or whatever. The limitations of those games, though, are that the entertainment only goes so far. Why compromise that experience?
"LA Noire is a fabulous, wonderful story and you could sit there for weeks exploring it in different ways. Why not be able to take that with you and continue the story? It's like a good book."
According to Bentley, Valve "really likes OnLive" and conversations are taking place between the firms about working closer together.
OnLive's Cloud Gaming service is due to launch in the UK this autumn.
BT has the exclusive rights to bundle OnLive together with its broadband service offerings in the UK, although customers will also have the option to order directly from OnLive to run over any UK ISP.