The duo worked together between 2008 and 2010, winning a treble comprising Serie A, Coppa Italia and Uefa Champions League titles in 2010, in addition to a league success in 2009.
Muntari, who recently joined Pescara on a half-season deal in January, also spoke about current manager Zdenek Zeman as well as Massimiliano Allegri, who managed him at AC Milan.
''Mourinho? I owe so much to him," Muntari said, as reported by GianlucaDimarzio.
"He gave me the chance to play in a big club like Inter Milan and I won the treble in 2010. I thank him for a lifetime.
''Allegri? I still have a great relationship with him. Sometimes we feel great working with such top coaches.
''Zeman is like a father although speaks little. With him, you cannot complain.
"You just have to follow him and train. I had met him before when I was young.
''My future? What counts now is the present and it is not something to give speech on.
"I want to help my club [Pescara] in the league in order to maintain our topflight status. I repeat, nothing is decided yet but I will continue to play."
Muntari has also played for Serie A outfit Udinese, from whom he joined Portsmouth in the English Premier League in 2007.
In 2011, the 32-year-old had a loan stint with Sunderland. He was also on the books of Al-Ittihad Jeddah of Saudi Arabia in 2015-2016.