The Liverpool Echo claims that progress has been made over the fee to be paid, and agreement has essentially been reached, so the 21-year-old French forward is now a step closer to becoming an Everton player at last.
Barry's transfer has become the latest transfer saga affecting the Toffees and one that is more important still after the failure of their pursuit of Liam Delap. For a time, it seemed as though this one might fall through as so many other possible transfers have in the past.
However, if this story is correct, it does look increasingly likely that the Blues will get this deal over the line very soon and Barry will become an Everton player.
Getting the Villarreal starlet in will be a statement signing. Perhaps it is not a huge one, but it does indicate that the club are serious about bringing in quality young talent that can help this Everton team finally begin to compete in the top half of the Premier League.
If and when he arrives, though, it will place further question marks around the future of the Toffees' existing strikers, the Portuguese pair Beto and Youssef Chermiti.
Beto has been David Moyes' first choice at centre-forward since he took over from Sean Dyche and did enjoy a purple patch under the Scot, but has not totally convinced that he can be that number one striker the Blues desperately need and score enough goals over the course of a whole campaign.
Chermiti has not had much chance, and given his age and lack of experience, it makes sense for him to perhaps go out on loan, if Everton have at least two or three other forwards in the squad.
As a result of all these stories floating that Beto will become surplus to requirements if Everton get Barry and another striker in over the next few weeks.
Leeds United are said to be the main potential suitors for the player if he leaves Merseyside, with the newly promoted Yorkshire side apparently readying a firm bid.
Personally, although Beto should not be the club's number one choice, I think he could still be a useful reserve and a player who does seem to suit Moyes' way of playing.
In addition, Barry has previously often played in a 4-4-2 formation alongside another striker, and it could be a potentially effective partnership to try.
Regardless of this, if the young Frenchman arrives, he needs pace and width and good quality service into the box to be able to provide the most effective threat up front. That means more attacking signings are essential.