Duarte played under Mourinho when he began his career with Uniao Leiria in 2001 and has been strongly influenced by his fellow Portuguese.
"He congratulated me and said he is not surprised (that we reached the semis)," Duarte told BBC Sport.
"He is like a father for me, and for the young Portuguese coaches."
Duarte added: "For me, for us, Mourinho is a good reference so when he called me I was very happy."
I'm very happy because every day my team is better. We are playing very good football
Although Duarte is still searching for a first trophy while Manchester United boss Mourinho boasts 23, what do they have in common is that both began their coaching career with Uniao Leiria.
Duarte, who spent a decade at the club between 1995 and 2004, was Mourinho's centre-back as Uniao Leiria finished seventh in 2002.
"Mourinho is very important in my career because 15 years ago, he changed the mentality of Portuguese football. The training and the mentality of the players changed," Duarte said.
Of the four semi-finalists at this year's Nations Cup in Gabon, the Burkinabe - surprise runners-up in 2013 - are the only side to have never won the title.
After a season in charge of Leiria, Duarte instantly moved to Burkina Faso - leading the side between 2008 and 2012.
After spells with French side Le Mans, Tunisian club Sfaxien and Gabon's national team, the 47-year-old returned to take charge of the Stallions in 2015.
Now, they are impressing observers with the quality of their football - particularly when beating Tunisia 2-0 in Saturday's quarter-final in the Gabonese capital Libreville.
"Egypt have a good team but I have a good team, too," Duarte explained.
"I know this team from 10 years ago but back then, we didn't have so many good players because they were all playing in second or third divisions. Now everybody plays in a premier league.
"The success of the team is hard work and humility.
"I'm very happy because every day my team is better. We are playing very good football and this is very important for me."

The 34-year-old's deal is the third short-term contract he has signed since joining the Championship club last summer after four injury-plagued years.
Barker only made five substitute appearances, but helped the Brewers avoid relegation and boss Nigel Clough sees him as a valuable squad member.
"I am not signing as a player expected to play 90 minutes or a couple of games a week," Barker told BBC Radio Derby.
"Six months is perfect. Physically I feel no different than I did in my mid-20s. I am fit enough and can still do sessions like everyone else. But I have a reaction with my knee so have to be careful."
The former Derby County centre-back said his aerial ability means both he and Clough are sure he can continue to contribute.
"There is definitely use for me in certain games," Barker added. "To play 90 minutes is a little bit too much, but you never know.
"If pre-season goes well and I am fit and able that would be lovely, but it is not something the gaffer and me are expecting."
Burkina Faso coach Paulo Duarte has revealed Jose Mourinho has phoned him ahead of Wednesday's Africa Cup of Nations semi-final against Egypt.
[NEXT_CONCEPT]
Defender Shaun Barker has signed a new six-month contract with Burton Albion.