Carlos Ayala has not been heard from since 15 April when he arrived in the city of Cucuta, 400km northeast of Bogota, local police chief Colonel Jose Henao said.
"It's a rather delicate situation," European Union spokeswoman Francoise Le Bail said on Tuesday.
"We have some indications, but we have to be careful about what we say."
Investigators were trying to trace Ayala's movements after he arrived in Cucuta, and Henao said it was too early to speculate about whether he had been kidnapped.
The 59-year-old has been based in Bogota since 2003 to work on social development issues.
Colombia is the kidnapping capital of the world, with some 1500 people abducted last year, mainly by leftist rebels for ransom.
In a statement, the European Commission said it was deeply concerned by Ayala's disappearance and urged authorities to do everything possible to ensure his safe return.
Cucuta is the capital of Norte de Santander province, one of Colombia's main cocaine-producing regions that is being fought over by Marxist rebels and their right-wing paramilitary foes.
Colombia's 40-year-old conflict kills more than 3000 people every year.