Cohen - who took over from Jay Hunt in the position - made the comments following reports that Vernon Kay was being lined up to take over the 82-year-old's presenting duties alongside his wife Tess Daly.
"Bruce is a great entertainer and if he wants to keep doing Strictly, the job is his," The Mirror quotes Cohen as saying. "He is on holiday at the moment but when he gets back we will sit down and discuss things. All the speculation about other presenters is confusing, because we haven't approached anyone else. That is the truth. We will be speaking to Bruce when he gets back."
He went on to hint that Forsyth - who was honoured with a 'Special Recognition Award' at the National Television Awards last week - could celebrate his 70th year in the industry with a special show next year.
"Do you realise he has spent almost 70 years in show business? The guy is incredible. Would we like to do a programme about that anniversary? Yes, for sure," he said. "I think the BBC did a show when he turned 80, but if we could possibly make something different and Bruce wanted to, we would love to discuss that with him as well."
> Forsyth: 'Kay would be great Strictly host'