The 29-year-old left European champions Bayern Munich in search of a new challenge during the recent window, with Liverpool winning the race for his signature in a deal worth around £25m.
A number of Europe's other top clubs were credited with an interest in Thiago, and his father - former Brazil international Mazinho - has confirmed that PSG made a late attempt to hijack Liverpool's deal before instead signing Thiago's brother Rafinha.
"I had spoken with Leonardo some time ago, but it was for Thiago. Leonardo wanted to sign him for PSG, but Thiago had already made a deal with Liverpool. We then talked about Rafa, but he was not part of Leonardo's plans at that time," Mazinho told France Football.
"I think he must have thought about it, that he saw the nature of the opportunity and it would be a blow to sign him. When he started talking again, Leonardo had changed his mind. And it all sped up on the last day. It was Monday that we had to work hard to convince both clubs.
"We were scared, but thank God, five or six hours before the deadline, we made a deal. Leonardo wanted Thiago, he got Rafinha. And for Rafa, it was a dream to join such a club."
Thiago has so far been limited to only two appearances for Liverpool, having tested positive for coronavirus after his debut and then picked up an injury on his return.