Carrusel Deportivo says negotiations have extended beyond the end of the transfer window because Atletico were given special dispensation to sign a player after they lost Thomas Partey on last day of the market.
Kondogbia moaned earlier this month that Valencia had gone back on their word but a deal has finally been reached for him to move to Atletico, who will pay around 20 million euros.
The midfielder is due in the Spanish capital for a medical on Sunday.
Atletico coach Diego Simeone wanted another midfielder after the departure of Thomas. They were powerless to stop the Ghana international leaving after Arsenal paid his release clause.
Lucas Torreira was signed but Atletico were granted an extension by La Liga to sign another midfielder, with Kondogbia their No.1 target from the start.