Ecclestone, 83 and facing legal challenges including a $100 million damages claim in London over a 2005 business deal, told British newspapers in Brazil last week that he would like to hand over one day to Horner, 40.
"Christian would be ideal," he was quoted as saying.
Horner, who has led Red Bull and German driver Sebastian Vettel to four successive constructors' and drivers' championships, subsequently played down such talk and Montezemolo made his feelings clear to Italy's RAI television.
"Ecclestone sees Horner as his successor? As the years go by, he more and more enjoys making jokes and I'm happy he still has the desire to do so," the Italian said in the interview broadcast on Tuesday night.
Montezemolo also addressed Ferrari's failures over a season that saw the sport's oldest and most successful team finish third in a championship dominated by Red Bull.
He denied that Ferrari had lost any of their political clout, highlighting that they alone among the teams had a historic right of veto.
"More political weight than that is impossible," he said.
Montezemolo said 2013 had been "definitely a year to forget" and demanded answers as to why the team had failed to develop the car in the second half of the season when Vettel won a record nine races in a row.
He criticised the Interlagos race stewards for a drive-through penalty imposed on Ferrari's departing Brazilian Felipe Massa that cost the team a chance to leapfrog Mercedes in the championship.
"Every so often the gentlemen who come to the races to act as stewards make decisions that are a bit ridiculous and anachronistic," he declared.
"One needs to be careful that we maintain credibility, for the work of the teams that invest money and for the drivers who risk their lives."
Massa was penalised for crossing a white line at the pit lane entry with all four wheels, a transgression that drivers were warned about before the race by the governing body.
Mercedes team boss Ross Brawn said after the race that his drivers had reported Massa was consistently breaking the rules.
Montezemolo hailed Fernando Alonso, overall runner-up, for a great season but only gave him eight out of 10 rather than a maximum score as an incentive for next year, when 2007 champion Kimi Raikkonen returns as Massa's replacement.
The Finn, he said, "will give us a boost and should bring the points we were missing this year".
The president warned both drivers that the team always came first, however, even if double world champion Alonso was possibly the strongest racer he had ever met.
"None of our drivers could ever hurt the other one," Montezemolo declared. "I am sure they will help one another."