Marca, Diario AS and Cadena Ser all say that the Spain international will sit out four games due to his insults to the referee and a further four for grabbing his arm.
There had initially been suggestions that the former Chelsea player would receive a 12-game ban, but this decision is set to rule him out for the remainder of the campaign.
The striker was shown a straight red card during Saturday’s loss at Barcelona by referee Gi Manzano, who stated in his post-match report that Costa insulted his mother, and that was the reason for the dismissal.
Costa has denied using a derogatory term towards the referee and his manager Diego Simeone has came to the defence of his striker:
“The sanction seems to me to be greatly exaggerated,” Simeone told reporters on Friday, as cited by Marca.
“Costa’s season was not good but that is as a result of injuries, I repeat – because of injuries.
“We hope he comes back for us strongly in pre-season and finds his rhythm with us once more.”