Albion's rejection of the bid is also expected to scare off Everton,who are not willing to offer anymore than £4million for the midfielder.
Koumas is currently on a break and has not made any official comment about his future, but has admitted his desire to return to the Premiership.
A joint offer for Koumas and former striker Nathan Ellington has been rumoured, but knowing Baggie Chairman Jeremy Peace, it will be rejected unless it is "head turning money".