Antony was sold by Manchester United to Betis after his successful six-month loan last season.
He recalled to Globoesporte: “Dude, I’m going to be completely honest with you right now, it really shook me up.
“We’re talking about a global giant, Bayern Munich, where there is a coach with that kind of history.
“Vincent Kompany called me and we had a conversation. He was super polite to me, said he always really liked my football, and this was at 11pm (on deadline day) a little after 11pm.”
He added: “What weighed heavily on my decision was that I’m a family man. It’s about looking out for my children. Lorenzo (his son) loves this place, loves this city.
“When we were on vacation in Brazil, without knowing anything, he always asked, ‘Dad, when are we going back to Spain?’”
On his departure from United, he added: “I don’t hold any grudges, I’m not angry at anyone there.”