The Portugal midfielder is now emerging as the central piece of their rebuild following Antoine Griezmann's departure for MLS.
Speaking this week, Alemany was asked directly whether Silva was a target. His reply was brief but telling.
"A great player, no doubt about it."
Alemany also addressed the broader approach to a transfer window shaped by the World Cup.
"Each club has its own recipe. The market is longer because of the tournament. We are going to act as if there were no World Cup. It will not condition us. We have clear objectives, we know what the coach wants, and I am convinced we are going to improve."
Bernardo Silva leaves Manchester City at the end of his contract this summer after nine seasons, having won six Premier League titles, three FA Cups and the Champions League. The 31-year-old Portugal midfielder had been linked with Barcelona, but the Catalan club declined to pursue him.
Juventus were considered frontrunners until Atletico Madrid made their move. According to Marca, a two-year deal with a one-year extension based on objectives is on the table, and the signing has backing at all levels of the club.
Alemany indicated that Atletico had already been active in the market for some weeks and would continue to accelerate where possible.
"There are circumstances like big release clauses in any situation," he said. "We have to work with independence from what happens at the World Cup. The market is open for a long time, but steps need to be taken — and if they can be accelerated, all the better."
Bernardo Silva's connection to Spain, where he has family and personal ties, has been cited as a factor in Atletico's favour. He is understood to want to remain in Europe and compete for major honours rather than move into a more comfortable environment. The Metropolitano, with Champions League football secured for next season, fits that profile.