Lucas Hernandez said he turned down the chance to leave Atletico for city rivals and La Liga giants Real Madrid.
The France defender's younger brother Theo is already on Madrid's books, having joined from Atletico in 2017.
Deals between the Madrid clubs are unusual but Theo's move was more palatable as he had never played for Atletico's first team.
Lucas, though, said he could not bring himself to follow his sibling to the Santiago Bernabeu, although the 22-year-old would not rule out leaving Atleti in the future.
"I didn't pay too much attention [to the offer]," Lucas said to RMC Sport . "I was 100 per cent focused on my club, where I had recently signed a new contract.
"My agent told me about it. When he said there was an opportunity to go to Real Madrid, I told him I couldn't do that.
"Atletico are my club, a team who have given me everything. I'm an honest person and I couldn't go to Madrid.
"I hope I can stay here for a very long time, but football moves very fast. If an offer comes in that I can't refuse..."
Lucas started all seven games for France in Les Bleus' World Cup triumph at Russia 2018 and is in Didier Deschamps' squad for games against Iceland and Germany this month.