An initial 18-month deal, worth a reported 12 million euros ($16.6 million), has been renewed for a further season. That means league-leading Atletico could soon be parading Azerbaijan's historic slogan as Spanish and European champion in the Champions League, UEFA Super Cup and FIFA Club World Cup, played in Morocco in December.
Atletico's 3-1 win at Chelsea on Wednesday capped an important week for Azerbaijan's sports image, following its Euro 2020 bid and the announcement that Baku will stage a Formula One race next year.
Baku is also hosting the inaugural European Games in 2015, using a new Olympic Stadium the country hopes will one day stage the Summer Games.
The national Olympic body, led by President Aliyev, has twice been rejected by the IOC as a candidate.
"Slowly we can become a sports hub in Europe. (The European Games) shows that Europe is also trusting us," said football official Mammadov, a member of FIFA's social responsibility panel.
The sports world's faith in Azerbaijan is not shared by activists alleging restrictions on free speech and elections, plus corruption levels that are among the worst in Europe, according to Transparency International.
Mammadov pointed to financial and political stability, suggesting: "I don't see any reasons for some of the people to consider us as a negative."
Azerbaijan has such standing in football that FIFA President Sepp Blatter's first public duty on being re-elected in 2011 was going to Baku with UEFA President Michel Platini. They laid foundation stones at the stadium.
The country has yet to find much success on the pitch, though, although its national team can perhaps also target Euro 2020 as a competitor, with the new Nations League offering possible qualification through the Division Four playoffs. It plays the World Cup-bound United States in a friendly in San Francisco three days after the Champions League final, and its German coach Berti Vogts is then set to help U.S. counterpart Jurgen Klinsmann with his preparations for Brazil.
Azerbaijan is still trying to get a club team into the Champions League, with Baki and Neftci having previously been eliminated in the qualifying rounds. Neftci did play in the Europa League group stage last season and held Inter Milan to a 2-2 draw at San Siro.
"At least to compete in the Champions League group stages — I would say it is realistic," Mammadov said.