Amorim indicated that the decision could be expected within a few months.
Swedish manufacturer Saab's Gripen jet fighter is up against the Rafale fighter, made by French firm Dassault Aviation and US aviation giant Boeing's F/A-18 Super Hornet for a tender from Brazil to supply 36 multi-role combat aircraft.
The contract has been variously valued at between $4 billion and $7 billion.
"We are entering the final chapters," Amorim told the magazine Istoe. "I have an expectation that the matter can be resolved in this semester (first half of the year)," he said.
A senior Brazilian government source said Monday that President Dilma Rousseff would decide which fighter jet to buy after a visit to Washington in April and the French presidential election in May.
Amorim has previously said June is a likely date for the announcement.
Last year, Brazil delayed a decision on the purchase following a major budget cut, but the jets are needed to beef up the country's air force.
French Prime Minister Francois Fillon said before a visit to Brazil in December last year that he was confident the Rafale could beat off rival bids because the aircraft's technology was superior.
The Rafale was used in the recent war in Libya but the fighter has repeatedly lost out in tenders in countries including Singapore, South Korea, Morocco, and earlier this month, Switzerland.
India has selected the Rafale for its air force, but a deal has not yet been formalized.
French Defense Minister Gerard Longuet said last year that unless the Rafale can find a foreign buyer, the government will have to stop funding its production by Dassault.