The Venezuelan leader said that if Colombia built the base, his government would revive a decades-old territorial conflict and stake a claim to the entire region.
The US maintains a military base at the Pacific port of Manta in Ecuador, but Rafael Correa, Ecuador's president and an ally of Chavez, has repeatedly said he will not renew the 10-year leases when it runs out next year.
Chavez said that William Brownfield, the US Ambassador to Colombia, had suggested that the Ecuador base could be moved to La Guajira.
Diplomatic relations between Caracas and Bogota have come under increasing strain in recent months after Colombia unveiled documents allegedly showing that Chavez sought to arm and finance Farc, an armed anti-government group in Colombia.
Last week the US claimed the documents, contained on a laptop, were "authentic" and showed ties between Chavez and Farc.
Chavez, whose sympathies for Farc are well known, said the files had been faked by the Colombian government.
The computer files were found after Colombian forces mounted a raid inside Ecuador to kill a Farc commander at his camp across the border.
The raid sparked a regional crisis when briefly raised fears of war when Chavez threatened to send troops to the border with Colombia.