Guardiola officially confirmed his departure on Friday, ending a reign that produced 20 trophies including six Premier League titles and the Champions League. He will leave Manchester City after their final game of the season against Aston Villa on Sunday.
Speaking at his final press conference, Guardiola said Ferguson had been in touch the previous day.
"One of the biggest compliments I had: I got a message from Sir Alex Ferguson yesterday. That made me so happy," he told reporters.
When pressed on what was said, Guardiola smiled: "A Scottish accent, I didn't understand it. It was a voicemail. I will call him back. Congratulations for the trajectory and for what we achieved. It means a lot to me."
He added: "He is the greatest in this country. The tenure, the time, and for many, many reasons. I'm pretty sure Sir Alex will not call us the noisy neighbours again. We are the neighbours, just the neighbours. And I'm happy that he was there to watch."
The warmth of the exchange sits against a backdrop of sharp rivalry. Ferguson and Guardiola clashed when the latter managed Barcelona, with Manchester United losing the Champions League final to Barca in both 2009 and 2011. After the 3-1 defeat at Wembley in 2011, Ferguson was generous: "In my time as manager, this is the best team we have faced."
Ferguson retired in 2013, three years before Guardiola was appointed at City. By then the clubs were moving in opposite directions.
Guardiola arrived in Manchester in 2016 from Bayern Munich and transformed City from perennial challengers into the dominant force in English football. He did not just win titles. He won them in a way that forced every other club to change how they thought about the game.
A decade. Twenty trophies. One voicemail from the man he never quite got to beat.