Fresh news about the franchise is coming again from Rely on Horror. They've contacted Konami North America representative directly to ask about these rumors, and they have got a reply shortly after. In response, he said that both rumors aren't true.
But when asked to specify if neitherKeiichiro Toyama is working on a Silent Hill reboot with SIE Japan, nor that Kojima is working on a separate entry in the series is true, they haven't got the answer.
Still, in the mail they got, the NA representative said: “It’s not to say we are completely closing the door on the franchise, just not in the way it is being reported,” which does confirm that something is definitely happening around the Silent Hill franchise.
Earlier reports from January suggest that some kind of Telltale-type adventure is in the works, and that Konami is actively speaking with various developers in order to find out options and ideas for potential new entries into series.