It is reported the Latics will have to pay about £3.5m to sign midfielder Diame and centre-back Amaya from the Madrid-based second division side.
"We still haven't finalised negotiations with the English club Wigan Athletic for the transfer of our players Diame and Amaya," said a statement on Rayo's website, rayovallecano.es.
"The talks are very advanced, but there are still some loose ends remaining before the transfer can be completed.
"At this moment Diame and Amaya are still players of the first team of Rayo Vallecano."
Wigan have refused to comment on Vallecano's claims.
Wigan's Spanish manager Roberto Martinez has been linked with a number of names in his homeland but it has tended to be higher-profile players like Espanyol's Raul Tamudo.
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