The issue was thrust under the spotlight after it emerged that Manchester United's Belgium-born Adnan Januzaj has been earmarked as a future England international.
"It is an issue we need to look at," Dyke told reporters. "The idea that someone who is not born here can never play for England is a bit extreme. We wouldn't have Mo Farah if that was the case.
"We will discuss our policy again and make a decision. It comes down to saying what principles do we want to abide by; it is not a case of individuals. The FA is looking at what we feel is appropriate."
Arsenal midfielder Jack Wilshere sparked controversy when he weighed in on the debate, insisting that only English players should be able to represent the Three Lions.