In my experience you don't look for another deal elsewhere unless the deal you had is bad or doesn't seem like it's going to continue. I haven't heard anything about Kojima having been unhappy working with Sony, so that would suggest Sony haven't offered a deal for another game.
What makes you think he wasnt offered a better deal by a competitor?
As far as I know nobody tried to poach him while he was at Konami and in the end they seemed more than happy for him to go. He wasn't even looking to leave so if they had wanted to keep him they didn't even need to do anything, just maintain the status quo. They wanted him gone though.
He just seems much more like the type to go round cap in hand begging for the resources to create his games rather than somebody that's in demand. I wouldn't be at all surprised if that's how the Sony deal happened either, he was going round looking for somebody to help finance his new game and they were the only ones willing to help out, rather than they specifically sought him out. So if this MS rumour is true I'd assume the same.