Hodgson’s contract expires at the end of the tournament in France, with England on the brink of reaching the last 16.
They will top Group B with victory against Slovakia in St Etienne tonight after a last-gasp 2-1 win over Wales on Thursday.
Dyke said Hodgson’s contract is likely to be renewed if England impress in France, but Hodgson remains focused on Slovakia.
“It’s been raised many times before, it doesn’t make any difference one way or another,” he said at a press conference.
“My contract runs out after this tournament, that’s a fact everyone has known about for the last two years. On a regular basis it gets brought up – should I stay, do I want to stay, what should the FA do?
“Nothing changes in that respect. For myself and the players there is only one thing on our minds and that’s to win the next game and see how far we can go.
“We concentrate on what we can do and what we can do is work very hard in our preparation for the game we are about to play. One day, after our stay here ends, the FA will need to make a decision with what they want to do in regards to the future.”
Daniel Sturridge scored the injury-time winner against Wales after coming off the bench at half-time and he could replace the misfiring Harry Kane up front.
Leicester’s Jamie Vardy also netted when he was brought on at the break, but Hodgson insists he will not make changes for the sake of it, despite the duo’s second-half impact.
“I don’t think it’s absolutely necessary, the players are in good shape and I don’t think it would be a problem if I wanted to keep very much the same side,” he said.
“There are players who would like to play and knocking hard at the door, so I have the option if I want to refresh because everyone is anxious to get their chance. It’s really a question of what we would like to do rather than what we feel is necessary.”
And Hodgson dismissed any suggestion Tottenham striker Kane, who was substituted at half time against Wales, was tired after a long season.
He said: “I have spoken to Harry, he has been very good in training and I don’t think he is suffering more from a season than any other player. We have some players who have not played on a regular basis, maybe through injury or other reasons, but there’s no problem with him in that respect.
“Jamie and Daniel did very well and I’m sure they would like another chance. It’s a decision which has to be made.”
Captain Wayne Rooney has so far been deployed in midfield, with Kane leading England’s attack. Rooney is yet to score at Euro 2016, but netted twice when England beat Slovakia 4-0 in 2009 in their last meeting and is enjoying trying to create chances for the strikers.
The Manchester United man said: “They are great to have in the squad. Everyone has seen the quality of players we mentioned before the tournament. Whoever the manager decides to play is his choice, but we have players who can come on and change games.
“As this season has shown they are goal scorers. It’s important we try to get them chances.”
Meanwhile, Martin Skrtel has warned his Liverpool team-mates there will be “no such thing as friends” when Slovakia take on England.
The 31-year-old shares an Anfield dressing room with Daniel Sturridge, Adam Lallana, Jordan Henderson, Nathaniel Clyne and James Milner, with Raheem Sterling another former colleague, but will not be dishing out any preferential treatment in St Etienne.
“It’s not a normal situation for me, but we’re professionals and it’s all part of the job,” said the defender. “I know them and they know me, though there’s more to the match than just that.
“In a match like this there are no such things as friends. You can maybe be friends before or after the game, but not on the pitch.
“Everyone will be giving their all for their team and doing their very best to win the game. It’s a game between two nations, and England have got one of the best teams in the world.”
Skrtel might tend towards admiration for Hodgson’s squad, no surprise given he has spent eight seasons on Merseyside, but he also appeared to echo Gareth Bale’s recent inflammatory comments. Bale said prior to Wales’ 2-1 defeat that English players could not match the pride or passion of his side, a theme Skrtel appeared to pick up.
“The smaller countries have probably got more team spirit, especially when they come up against the big countries,” he said. “The pressure will be on the English, though I think they have enough experience to be able to handle it.
“It’s all going to come down to what happens on the pitch, and I think we can reproduce our performance against Russia [a 2-1 win].
“We showed heart, character and motivation.”