Dyke, the FA chairman, has proposed a new division be created between the Conference and League Two which would include a number of Premier League clubs' B teams.
The plan emerged from his England Commission which aims to increase the number of English players in the top flight, and Dyke says it would give young players more experience of competitive football.
But Bradford City chairman Mark Lawn said there was a "general consensus" among the 72 Football League clubs that the B league would not work.
Lawn, speaking from Portugal ahead of the meeting, told Press Association Sport: "Nobody understands how playing at Conference or League One level can help any player make it to play for England.
"There is a general consensus that it wouldn't work and would not be good for our club football either.
"The FA need to go to the Premier League and say they only have so many foreigners but they won't do it.
"The loan system as it is now works better - look at Tom Cleverley."
He started at Bradford, went to Manchester United when he was 12, went out on loan to Leicester, Watford and Wigan then went back to United and ended up playing for England.
"If they are going to end up playing for England they need to be playing at least at Championship level."
Blackburn managing director Derek Shaw echoed Lawn in claiming the current loan system works better than a B league would, and pointed out that Manchester United's young defender Michael Keane had been given "terrific experience" during his loan spell with Rovers last season.
Shaw told Press Association Sport: "We want to help the FA where we can
I'm personally not a big believer in this B league plan.
"We think the loan system can provide young players with terrific experience as happened with Michael Keane who came to us from Manchester United last season."
Football League officials are due to present an alternative proposal which would see some Premier League B teams play in an expanded Johnstone's Paint Trophy, which would include a group stage
It is unclear however whether that would interest top-flight clubs.
The meeting will also discuss the use of artificial '3G' pitches following the FA's decision to allow them in all rounds of the FA Cup, and the on-going dispute over financial fair play rules in the Championship.
Source : PA
Source: PA