Button to stay at Honda in 2009
The Brackley based squad is yet to confirm its race driver lineup for next year, amid the news that Bruno Senna – and another yet unnamed youngster – is to test at Barcelona later this month.
"I am absolutely convinced that if we, at Honda, give him the car that can do the job he can compete with Lewis," Fry, referring to 28-year-old Button, told BBC Sport.
Like Button, the Brazilian veteran Rubens Barrichello is also out of contract, and given Fry's latest comments therefore seems the most likely to make room for a newcomer.
"We are not hurrying to choose our drivers for next year," added Fry. "We can afford to wait until possibly just before Christmas."
Honda, who Fry admitted fielded a "weak" car this season, made a bid to attract Fernando Alonso, but it was announced on Wednesday that the Spaniard has re-signed with Renault for two further seasons.
Fry believes that Honda's increasingly poor finish to the 2008 season could pay off next year.
"We deliberately had a strategy of not doing much to this year's car, investing all our resources in next year," he said.