Former Manchester United chief executive David Gill was appointed as FIFA vice-president on Tuesday.
Dyke indicated that having Gill, also the FA's vice-chairman, in that role could persuade England to launch a fresh bid to host the World Cup.
"If David can assure us there's a proper system and it's fair then we could be persuaded," Dyke told BBC Sport.
"But at the moment the policy is straightforward - we don't bid while Mr Blatter's there."
England's last attempt proved fruitless as the 2018 World Cup was awarded to Russia, with the bidding process of that event and the 2022 instalment in Qatar having been the subject of an investigation into corruption - although Russia and Qatar were both cleared of any wrongdoing.
Dyke stated that any decision to start another campaign would depend on a host of factors.
"It depends on the timetable really. It depends on how quickly it has to be done," he added.
"But remember, you have to get an awful lot of people onside and that's not going to be easy in England now because a lot of people got badly scarred in the process last time.
"To make a bid you've got to get whoever is the government onside, and we don't know who that is yet because they have to underwrite it."
