The striker's club future has been the subject of much speculation this summer with Chelsea lodging two bids to acquire his services but it is understood he will not be handing in a transfer request and Hodgson is confident Rooney will not be distracted by all that is going on around him.
"He's an important player, he's been a fantastic servant for a good number of years now and he's still got the burning ambition to do well," he said.
"A fully fit, match-fit Wayne Rooney is important to the country but he's also important to his club and it's important to Wayne himself because the man loves to play football and he's the first onto the pitch and the last off it.
"I'm sure that (Manchester United manager) David Moyes had no worries or concerns whether he would do anything other than give his best or play to the very best of his ability last night just as I never had any concerns he would do the same for us.
"Because that is the nature of the man, that is the nature of the player."
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