Former England midfielder Barry is also believed to be wanted by newly promoted Leicester City and Everton where he spent last season on loan.
But a top Hammers insider revealed to ClaretandHugh exclusively: “Both deals are alive – Kouyate very much so but we still have to agree a fee.
“We will know more over the next 72 hours but the player remains very keen to join us.”
Barry, however, is now looking more likely to opt for Everton as he is well settled in the area and has the opportunity of playing European football with the Toffees
However, our source revealed: “The deal is still alive and we are doing our best . There’s still a squeak. We certainly haven’t given up on it.
“Koutaye is a big deal and we are working hard to get it done.”