He said he would like to see her continue her on-screen partnership with Tess Daly when the BBC1 programme returns in the autumn.
Sir Bruce announced earlier this month that he was stepping down from the live shows after a decade-long reign on the contest, presenting alongside Daly.
His departure has prompted speculation about the long-term replacement, but Tonioli - who has been with the programme since the beginning - backed Winkleman and Daly, although he was unsure what BBC bosses had in mind
The duo have been presenters on the Sunday night results show and have shown off their sparkling chemistry when Sir Bruce has taken a rest or been ill.
Speaking as he attended Brit Week in Los Angeles, Tonioli said: "Personally, when Tess and Claudia did the show they know how it works, they are part of the family.
"Strictly Come Dancing is almost like an institution itself now in Britain, and I would be very, very happy for them, but it's not my show. I don't have any power and it is the big bosses that will make the decision. But I'll be delighted to have Tess and Claudia - they are fantastic, they work very well together."
He went on: "The show is very, very strong. I don't know what is going to happen. I'm sure the replacement will be as good, as entertaining as Bruce but Bruce is such a legend especially in Britain, he's a national treasure, so you can never try to be another Bruce.
"I think it has to be something completely different. The girls did very well. Tess and Claudia did a fantastic job."