Dyke presented his proposals aimed at improving the future of the English game to club owners and executives.
But Football League chief executive Shaun Harvey says it was not popular.
"It's fair to say there is no appetite among clubs for the use of B teams or Strategic Loan Partnerships in the football pyramid," he said.
Dyke warns that failure to adopt his plans to improve English football could lead to a bleak future for homegrown talent.
At the heart of the FA commission's four-point plan is the creation of a new tier within the Football League to accommodate Premier League B teams.
There is also a call for a ban on non-European Union players outside of the top-flight, the development of "strategic loan partnerships" between clubs, as well as a reduction in non-homegrown players in Premier League squads.
Harvey admits that other aspects of Dyke's plans were more well received during a two-hour briefing at a conference in Portugal.
He added: "They did share his overriding concern about the development of young English footballers and supported a number of the report's other recommendations.
"We will continue to work with the FA to help find solutions that will be supported across the whole game."
Football League clubs have "no appetite" for Football Association chairman Greg Dyke's plan to set up a new tier for Premier League B teams.