Depor, league champions in 2000, have been targeted by the tax authority with an embargo on their income. Local media have reported in the past they owed the government a figure of around 34 million euros.
"Deportivo...have started the negotiations that preface a meeting with creditors and to reach an agreement on a re-financing package," Lendoiro told a news conference late on Thursday.
"The tax authority have embargoed practically all our income.
"The tax authority has received more than 20 million euros from us in 2012. Deportivo have offered to pay the outstanding debt over the next 10 years, if they lift the embargoes."
Lendoiro, president of Deportivo since 1988, was keen to stress that the Galician club was a viable business.
"Our income far exceeds our expenditure," he said. "Deportivo don't want to enter administration. They want to pay their debts with the tax authorities and their creditors."
The Spanish government said they were owed 750 million euros in unpaid tax bills at the start of the year, and reached an agreement with the football league (LFP) in April to help speed up the settling of these debts with a tougher stance.
Spain's tax agency has collected 329.9 million euros this year, with 305.1 million coming from clubs in the first division, according to an agency briefing note.
Some 130 million euros more is expected to pour into the agency's coffers this year, around 55 million of which is accounted for by embargoes placed on income from sources including audiovisual rights, ticket sales and lottery, the note said.
Depor, who spent last season in the second division, are 16th in La Liga with two wins from 10 games and visit Real Zaragoza on Saturday.
"It's up to me to make sure this doesn't affect the team," Depor coach Jose Luis Oltra told a news conference on Thursday before Lendoiro spoke.
"I haven't seen the players looking worried or lacking in concentration. I don't think we need to be alarmist about the situation."