Reports surfaced midweek that captain Rooney and Vardy had a dispute over the Twitter prominence of Vardy’s wife Rebekah, which could be an unwelcome distraction for the team.
“I haven’t got a clue what you are referring to. There are absolutely no problems in football terms between Wayne Rooney and Jamie Vardy,” Hodgson told British media.
“In fact quite the reverse, they are very close friends, both on the field and off the field. I have got no idea what you are referring to.
“I certainly would advise Wayne to give no comment to it, because it is obviously one salacious story that someone has managed to spin. It is of no interest to us.”
England have come under pressure after scoring three goals so far and Hodgson expected a difficult encounter against Iceland.
“The character of the Icelandic people, their determination, their ability to survive through hardships — I am certain that has been a major factor in their progress as well,” Hodgson said.
“But we know, perfectly well, that whether we title them favourites or underdogs, it is going to be a very, very difficult game for us and they are going to be a hard team to beat.”