The Reds pursued the Guinean midfielder for much of the summer transfer window having identified him as a top target.
Jurgen Klopp was unable to bring the highly-rated 22-year-old onto his books, but a club record deal has been put in place which will be pushed through in 2018.
A £48 million agreement will take Keita to Anfield and Mintzlaff says it was Liverpool’s determination not to miss out which ultimately saw them pip rivals such as La Liga giants Barca to a prized signature.
He told Sport Bild: "Barcelona enquired about the signing of Naby Keita.
"But it seems they were not as driven as Liverpool."
Mintzlaff also believes that the agreement eventually put in place has proved beneficial to all parties, with Leipzig retaining Keita for a Champions League adventure in 2017-18 while also generating the best possible fee for his services.
He added: "We wanted our focus to be 250 per cent on our triple burden this season, but it had become difficult for Naby.
"That way, we found a solution which gave the player back his security.
"Also, we were able to negotiate for a much higher transfer fee.”
Keita recently revealed to Goal that while he remains fully focused on his efforts at Leipzig, he is looking forward to making his way to Merseyside next summer.
He said: “I used to watch Xabi Alonso in the Champions League and Premier League when I was in Guinea and last season I got to play against him in midfield before he retired.
“When I think about things like this, it reminds me of how blessed I am, but also of how hard I’ve worked and far I’ve come. But this is only the start, I am never satisfied, I never get comfortable.”
That will be music to the ears of Liverpool and Klopp as they seek to see their persistence in a protracted chase handsomely rewarded.