The corporation boss said that changes will be made to the live stages of next year's competition after ratings plummeted to around 5m from a high of almost 12m during the blind auditions.
"We've had a few teething problems with the live shows," The Sun quotes him as saying. "We'll take away a few things from the live shows to tinker with for series two."
Defending the programme recently, Cohen insisted that the positive tone of The Voice is still "fresh" and "exciting".
He added: "We'll look at the end of the series but I think we're in a good place and I don't imagine mega-changes [for series two]."
Cohen has also said that he wants all four Voice UK coaches - will.i.am, Jessie J, Sir Tom Jones and Danny O'Donoghue - to return.
Voice creator John de Mol recently expressed his intention to make next year's live shows "more exciting".
"The role of the coaches can be bigger," he suggested. "In the semi-final, the coaches were just watching the talent perform. They had no influence. That's something we should change."
The Voice UK final airs tomorrow (June 2) at 7.20pm on BBC One.