"We decided that now was the ideal time for a change," Depor president Augusto Cesar Lendoiro said.
"In the coming hours, or perhaps tomorrow, we hope to present the new trainer," he added.
Spanish media reported that former Sporting Lisbon coach Domingos Paciencia was poised to take on the task of preventing Depor from going straight back down to the second division after Oltra led them back into the top flight last term.
The Galician team have fallen a long way since winning La Liga in 2000 and are one of many Spanish clubs crippled by financial problems.
Lendoiro said this month they would be forced into administration unless a deal with the Spanish tax authorities on outstanding debts could be hammered out before the end of the year.
With 17 matches played, Depor have managed only two wins and are bottom on 12 points. Their opening game of 2013 is at home to fourth-placed Malaga on January 5.