Strauss said he was happy with the system, which is currently in place.
''From my point of view the regulations the ICC have in place are perfectly adequate and I don't see any reason to change that,'' he was quoted as saying by Daily Telegraph.
England and Wales Cricket Board (ECB) has also reacted coolly to CA's suggestion.
''The ICC have the well-established principle of appointing neutral umpires for Test matches. It is a process that the ECB is comfortable with,'' an ECB spokesman said.
Cricket Australia had earlier suggested that a contest between the two best sides in the world should have the top umpires officiating.
''In a perfect world, it would be great for a series that will not only determine who wins the Ashes but could decide the world number one ranking to be officiated by the world's top-ranked umpires,'' CA Spokesman Peter Young had said.
Aussie captain Ricky Ponting had also concurred with his Board's suggestion.
''I'd just like to have the best umpires to umpire cricket around the world all the time. It's the highest standard of cricket we play so we have to have the best umpires in those games. Whether that means they are Australian, or two Pakistanis, or two Englishman, it doesn't matter to me as long as they are doing a good job in in the middle,'' Ponting had said.
Australian Simon Taufel is currently regarded as the best umpire in the world, while there are three other umpires from the two countries in the ten-member Elite Panel -- Daryl Harper and Darrell Hair from Australia, and England's Mark Benson.
If the ICC doesn't agree with Cricket Australia's suggestion, the umpires for the series will be selected from the six others in the panel -- Steve Bucknor and Billy Doctrove from the West Indies, Aleem Dar and Asad Rauf from Pakistan, Billy Bowden from New Zealand and South Africa's Rudi Koertzen.