Football Association chairman Dyke intends to look at ways of improving the England team set-up in the coming years, with the 66-year-old aiming to bring World Cup success by 2022.
Allardyce, who was present at the FA's 150th anniversary gala on Saturday evening, feels the asking price for any talented English player is inflated due to a limited number making the grade.
"The thing is, when something becomes a rare commodity it becomes very, very expensive," he said.
"There are a huge amount of young players in this country who don't quite hit the heights that they used to.
"If the report that the chairman of the FA is going to do will have some bearing on that I will only be too glad to accept it."
Allardyce has been praised for giving Ravel Morrison his chance in the West Ham first-team this season and the former Newcastle boss feels there are some talented youngsters emerging but their progress is being stunted by cheaper imports.
"It runs greater and deeper than the FA," he added.
"Foreign players love to play in this country and play in the Barclays Premier League and they are often not as expensive as some of the players that we have here because they are a rare commodity.
"We are forever talking about it and let's hope we can do something about it over the next five to 10 years. There are some exciting young players playing in the Premier League at the moment and they are developing, let's hope that carries on."
Even English clubs at the very top of the game and playing in European competition are having to pay vast sums for English players due to UEFA's ruling on the number of homegrown players in a squad, another reason Allardyce believes their respective prices have rocketed.
"There is the homegrown player [rule] as well which has upped the value of a player now when he is so young," he said.
"I had Phil Jones when I was at Blackburn and he ended up going [to Manchester United] for circa £20million with less than 30 games under his belt.
"Arsenal bought Alex Oxlade-Chamberlain for a huge amount of money and before that Theo Walcott.
"Manchester United bought Chris Smalling from Fulham before he had played even 10 games I think so it shows you how expensive it is to get young players who have been brought up in this country and until we start developing more of those they won't get any cheaper."