Roy Hodgson insists he only wants players who are fully committed to playing for England after handing a first call-up to Ivory Coast-born winger Wilfried Zaha for Wednesday night's clash with Sweden.
Former Chelsea star Didier Drogba has been amongst those trying to persuade Crystal Palace winger Zaha to opt for the country of his birth.
But Hodgson feels there is "no choice to be made" for anyone who gets the call-up to represent the Three Lions
He said: "It is very simple. England, for me, is very important. To be asked to play for England is a major honour and a major feather in people's caps.
"I am not interested in people who are deciding whether England is where they want to be.
"When people are called up I expect them to come running, get on a bicycle and cycle to the training session if they have to, then shake hands with everyone and tell them how happy they are to be there."
He added: "There is all this nonsense about players receiving phone calls and being enticed away. If they are going to be enticed away, they are not the right player for us.
"But Wilfried has played for England at Under-21 and Under-19 level. It seems to me fairly obvious if you want to do that and are happy to accept a call-up to the first national team, that is where you want to play."
Zaha is not the only player operating in similar circumstances in the current England squad.
The Football Association expect FIFA clearance for Arsenal defender Carl Jenkinson to feature at some point on Wednesday night after he had previously represented Finland at Under-21 level.
Liverpool midfielder Raheem Sterling, despite being handed his debut against the Swedes, is also eligible for Jamaica.
Hodgson said: "You can see it as a problem or you can see it as a blessing to have so many players capable of playing for England.
"If they happen to fall by the wayside, there will be somewhere else for them to go.
"I would expect players who have spent the best part of their life in England - and the whole of their football education has been in England, if they get a chance to play for the national team, they will.
"But I wouldn't stand in anyone's way if England didn't mean that much to them and they would prefer to play for the country of their parents' birth. I made that clear to Jenkinson."