It was claimed in April that Microsoft was in talks to sign the next game from the Japanese designer best known for the Metal Gear Solid series.
It marks a significant development in negotiations, although the deal is still to be finalised, according to the site.
“The deal is so close that Microsoft has begun preparing for what Kojima will need to make his new game,” the report claims.
Earlier this month, Xbox Game Studios appointed Portal and Left 4 Dead designer Kim Swift as senior director of cloud gaming, reportedly with a view to helping bring Kojima’s game to fruition.
Kojima has previously expressed a desire to explore a “new format of game” enabled by cloud platforms.