Hodgson stepped in to douse the claims as Rooney was asked about reports asserting he had grown concerned by the profile, particularly on social media, of Vardy’s wife Rebekah during the tournament.
“I haven’t got a clue what you are referring to,” said Hodgson. “There are absolutely no problems in football terms between Wayne Rooney and Jamie Vardy, 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 and 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 are seeking only their seventh victory in the knockout phase of a major competition since the 1966 World Cup when they face European minnows Iceland, while the winners will play France in the quarter-finals on Sunday.
Despite their lack of tournament pedigree, Hodgson was keen to convey his admiration for the Scandinavians, who are playing in their maiden European Championship and are the smallest nation to ever qualify for an international tournament.
“I think they owe a great debt to [joint-manager] Lars Lagerback. I don’t know the young Icelandic coach [Heimir Hallgrimsson] but I am sure he has played a big part as well,” added Hodgson.
“They have the ability to organise a team, get the maximum out of them and make them unbelievably difficult to beat, and also to engender a work ethic which is not seen every day.
“The character of the Icelandic people, their ability to survive through hardships – I am certain that has been a major factor in their progress as well.
“We will have to accept the title of favourites, and they can go into the game as underdogs. But we know that whether we title them favourites or underdogs, it is going to be a very difficult game and they are going to be a hard team to beat.”
Rooney, meanwhile, insisted he had no worries over Raheem Sterling’s state of mind after it emerged that new Manchester City boss Pep Guardiola had telephoned the former Liverpool forward following criticism of his performances.
“From what I have seen, his state of mind is fine,” said Rooney. “There is no issue with Raheem at all. His attitude has not been questioned by us. If anyone is questioning his attitude or his state of mind, they would be mistaken in having that judgement.”