Arsenal face Wigan on Saturday in an FA Cup semi-final, while Hull will take on Sheffield United on Sunday for a spot in the final as well.
Winterburn believes Arsenal have too much quality to miss out on lifting the FA Cup at the end of May, which would be their first trophy since they won the same competition in 2005.
"Well they're favourites. They're huge favourites. You can't get away from that," the 50-year-old told PERFORM.
"I mean if you look at the teams left in the competition, they're there on their own merit but when we look at squads and if we say, 'right, we're going to look at the squads and analyse them all, who is going to win this competition?' 100 people are going to say Arsenal, you wouldn't say anything else."
Winterburn won three league titles with Arsenal and two FA Cups and understands that the club is in a different position now with their much-publicised struggles to lift a trophy.
The former left-back concedes that pressure could affect Arsenal against holders Wigan or, if they make it, in the final against either Hull or Sheffield United.
"The pressure is on Arsenal simply because they are the overwhelming favourites for the FA Cup but also, put into that conundrum, as we're already been talking about, there hasn't been a trophy for such a long time," Winterburn said.
"So those players haven't got to fear that, they have to embrace it and say 'this is the time to end it, this is the year we can stop everybody talking, we can win that trophy and then hopefully we can really give a big push in the next couple of years to what the fans really want, and that is the Premier League title back' or a fantastic run in the Champions League and getting to a final."
Looking ahead to this year's World Cup finals, Winterburn believes England manager Roy Hodgson has a dilemma when looking at the left-back position.
Winterburn, who represented England twice, believes Hodgson might be better off taking Leighton Baines and Luke Shaw to Brazil and leaving ageing stalwart Ashley Cole behind.
"I think there is a massive conundrum for Roy Hodgson to decide how he sees the two places into three," Winterburn said.
"Is he just looking at the World Cup? If he is then he might just take Ashley Cole and Leighton Baines.
"If he's looking and saying, 'well, I could trust Luke Shaw to play because if Baines gets injured, I could give him that experience of being around a major tournament' - that's got to be a major benefit for England and player coming in for the next four, five, six, maybe even 10 years.
"It depends where Roy Hodgson thinks he is for England and what he is trying to achieve."
