Arsenal midfielder Wilshere has criticised the fact Manchester United's Adnan Januzaj, who was born in Belgium to Kosovar-Albanian parents, could, under FIFA rules, eventually represent England through residency.
"It is an issue we need to look at," Dyke told reporters on the fringes of a Leaders in Football business conference at Stamford Bridge.
"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," Dyke said in reference to Britain's double Olympic and world champion distance runner who was born in Somalia.
"We (FA) 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," he added.
Januzaj, who could also play for Turkey thanks to his grandparents and Serbia, has not won a cap for any country and would have to wait until 2018 if he wanted to represent England.
"If you've lived in England for five years, for me, it doesn't make you English. You shouldn't play," Wilshere was quoted as saying by British media on Wednesday.
"If I went to Spain and lived there for five years, I'm not going to play for Spain. For me, an English player should play for England really," added the midfielder, who is in the squad to face Montenegro in Friday's World Cup qualifier.
His comments provoked a Twitter exchange with England cricketer Kevin Pietersen, who was born in South Africa.
"Interested to know how you define foreigner...? Would that include me, (Andrew) Strauss, (Jonathan) Trott, (Matt) Prior, (golfer) Justin Rose, (cyclist Chris) Froome, Mo Farah?" Pietersen asked Wilshere.
The midfielder replied; "With all due respect Mr Pietersen the question was about Football! Cricket, cycling, Athletics is not my field!".
Pietersen responded; "Same difference.. It's about representing your country! IN ANY SPORT!", to which Wilshere replied; "I agree that's exactly what I was saying..."
Januzaj hit the headlines after scoring twice for United in their 2-1 Premier League win over Sunderland last weekend and his performances have caught the eye of England manager Roy Hodgson, who has said the 18-year-old was being monitored.
England Under-21 manager Gareth Southgate compared the situation to that of players like Pietersen in the national cricket team.
"We seem to have embraced the cricket team that has won the Ashes, but it is a really interesting, philosophical debate," the former England defender said.
"It's a difficult one. He's (Januzaj) not played for anyone else.
"I'm torn with it. The world is changing. People move and work abroad. It is important to know why someone wants to play for you."