Ferrari issued a statement earlier this week dismissing as "totally without foundation" media reports in Italy that Binotto was set to be replaced by Alfa Romeo team boss Fred Vasseur (54).
Binotto said Ferrari's decision to respond to the reports was made by him and Elkann together.
However, he stopped short of categorically stating he would be in his current job at the start of next year.
"Obviously it's not down to me to decide but I'm pretty relaxed," Binotto told reporters at the season-ending Abu Dhabi Grand Prix.
"The reason why I'm relaxed is that I always (have) open, frank and constructive discussions with my bosses, with my chairman, not only in the short term but the medium and the long term.
"When these speculations were out, I had a chat with my chairman John Elkann.
"We discussed openly what was the best way to move forward and we decided to release a statement was maybe the best way to close any speculation and clearly show that speculation is totally with no foundation."
Ferrari, whose drivers are Charles Leclerc (25) and Carlos Sainz (28), returned to competitiveness this season after two years in the doldrums.
The team, winless in 2020 and 2021, have won four races this season but their early promise as title favourites fizzled out due to reliability problems, strategy errors and driver mistakes.
Red Bull have won both the drivers' and constructors' titles, with now double world champion Max Verstappen (25) gunning for a record-extending 15th race win at this weekend's Abu Dhabi finale.
Ferrari, meanwhile, are in danger of dropping to third overall in the team standings, behind Mercedes, with early-season title favourite Leclerc also at risk of falling to third in the drivers' standings behind Red Bull's Sergio Perez (32).
Binotto said he felt Ferrari had achieved their main objective, which was to get back into the fight at the front but he acknowledged there was room for improvement.
"Yes, there are still a lot of things that we need to progress, weaknesses have been shown," he said.
"But I'm pretty sure that as we did in the past, we will review, we will try to address them."
