The announcement came following several months of speculation about possible partnerships, including with Delta Air Lines Inc and Panama's Copa Airlines.
"The board of directors of Avianca has authorized Avianca to carry out all the analysis and other steps that are required for a potential strategic-commercial alliance with United Airlines," the company said in a statement to Colombia's financial regulator.
The terms of the alliance are "pending negotiation", the company added.
Avianca has previously said it was analyzing partnership proposals in an effort to speed up growth.
United Continental was not immediately available for comment, outside of normal business hours.
Avianca's controlling shareholder, Synergy Aerospace Corp, will offer financing of up to $200 million to the company, the statement said.
Synergy will also be seeking to merge Avianca Holdings with OceanAir Linhas Aereas SA, which it controls, "under fair and reasonable terms for both companies", it added.
Avianca operates flights in Colombia, Peru, Ecuador, Central America and the Caribbean. The company transported 29.5 million passengers to 105 destinations in 2016.
Reuters |Reporting by Nelson Bocanegra and Julia Symmes Cobb; Editing by Muralikumar Anantharaman