A Spanish government crackdown on outstanding tax bills has seen Depor, La Liga champions in 2000, hit with an embargo on their income which has brought the issue to a head.
Local media have reported around 34 million euros is owed to the taxman, of a total debt which sits at over 100 million euros.
"Either we reach an agreement with the tax authority before the end of the year or we go into administration. We cannot wait any more," Lendoiro told a news conference, after a meeting with the squad and the players' union (AFE).
Lendoiro said the club remained a viable proposition and that they were keen to honour their debts in full.
"Depor have two negotiations running," Luis Rubiales, president of the AFE, told reporters.
"One is to reach an agreement with the tax authority to lift the embargo and reach a medium to long term solution. The other is to enter administration."
Depor won promotion back to the top-flight last season but have struggled on their return and lie bottom with 12 points from 16 games.