Despite his record breaking goalscoring haul over two seasons with Sporting CP, many of Winterburn's fellow pundits believe the Swede will struggling in the Premier League given his modest spells with Brighton and Coventry City.
But Winterburn likes what he's seen in preseason and told Tribalfootball.com: "Well, for the past three years I've been crying out for a centre-forward, so I certainly hope he scores goals or we're all in trouble!
"At the moment, I'm not sure, but I don't think he's 100 per cent fit in terms of being up-to-speed with the rest of the team after coming in later than the others. I think Arsenal are pumping a high level of work into him.
"But if Arsenal and the players around him adapt to his strengths, I have no doubt he will score goals.
"Now, come back to me in six months and he hasn't scored... then I'll change my mind! But I think he's got the power, the talent... and a terrific shot. We saw on the weekend with his header, he has excellent movement.
"But let's see halfway through the season if myself and the supporters are still as excited as we were a week and a half ago."
Time to deliver
Indeed, Winterburn insists what Gyokeres achieved with Sporting is now irrelevant, it's now about performing in an Arsenal shirt.
He added, "I've always said, it doesn't matter what you did, how you played, how many you scored at your other clubs, it's all about what you are going to do for my club.
"It doesn't matter what went on before, you need to deliver for my club. Gyokeres has come in and will score goals, I have no doubt about that."
- Nigel Winterburn was speaking to Tribalfootball on behalf of NewBettingOffers.co.uk