Such a move would formalise the continental and political groupings to stage the two World Cups with the battle for 2018 being fought out between European countries and 2022 a contest between the United States and four rival Asian bidders.
At present, England, Russia, the United States and joint bids from Spain/Portugal and Netherlands/Belgium are bidding for 2018 - but they are also, technically at least, in the race for 2022.
Qatar, South Korea, Japan and Australia are concentrating on 2022 - but if the U.S. pulls out of the 2018 race, none of the Europeans would bid for 2022 as one continent cannot host successive finals.
Dein told a media briefing in central London, he expects the U.S. to pull out of the 2018 fight soon.
"Michel Platini (the UEFA president) believes that 2018 should come to Europe and we believe that is our strongest case.
"We are sure it won't be long before the United States will withdraw from 2018 leaving themselves a run on 2022.
"We are not really interested in 2022, consequently we will almost certainly withdraw from 2022, leaving us with a European battle."
The United States hinted last month that they would almost certainly withdraw their 2018 candidature.
Platini said last month he was determined to bring the World Cup back to Europe in 2018 following the last European World Cup in Germany in 2006 and there now seems little doubt that this will happen.
Dein added: "Of course Michel Platini has a vote, I don't know how he is going to vote, all I know is that he wants the finals to be in Europe."
FIFA, world soccer's governing body, will decide which nations will host the 2018 and 2022 finals in Zurich on December 2 and the bidding nations are gearing themselves up to secure the votes of the 24 men on the executive committee.
"We have been in six countries in the last 13 days and we desperately want to win the right to stage the World Cup," said Dein.
"We are passionate about it and believe it will be a sporting success, a social success and a financial success and that is the message we want to get to everybody and the executive committee members."
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