Hodgson has spent most of his time since taking over on July 1 talking about players who are leaving or reported to be leaving, the latest being Dirk on Wednesday.
The Englishman dismissed that prospect out of hand despite Kuyt's agent claiming he wanted to move to Inter Milan and the player himself pledged his commitment to the club after last night's 2-1 Europa League play-off victory over Trabzonspor.
"We have to be forgiven for getting irritated by agents stirring things up even more," said the 62-year-old, who has mixed feelings about the imminent closure of the transfer window as it will stop speculation about his players but leaves him little time to buy reinforcements.
"It is bad enough if there is a genuine offer and a genuine problem to solve but it is even worse when you are constantly batting away things you shouldn't even be talking about.
"When the window closes then every press conference is about football and football matters rather than 'X's agent is saying this and is there any truth in it?' and you are trying to diplomatically answer the question without offending too many people."