Representative Guido Albers hinted this week that the outgoing Feyenoord coach would be interested in taking over at the Welsh club, who appointed Monk as Michael Laudrup's replacement in February.
With Swansea just four points off the relegation zone with 10 games remaining, Monk claims he is not interested in such rumours.
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"I don't care. It doesn't affect me," Monk told Wales Online. "What can I do about it? Nothing.
"You can say it is disrespectful but he [Koeman] probably does not know me from Adam, so he is not concerned about my feelings and I am not concerned about his feelings.
"I have to just get on with the job and do it properly. Whatever happens, I want to hold my head high that I have done the job properly and done all I can to take the club forward. That is all I can worry about."
Monk has endured a mixed start to his coaching career - picking up his sole win in the derby against Cardiff City.
While reaffirming his desire to secure the job on a long-term basis, he revealed no conversations regarding that topic had taken place with chairman Huw Jenkins.
"I've had no deep talks with the chairman, no chats beyond this season," he added.
"Of course, I want the job - I've been doing my [coaching] badges and my connection with this club means I want to manage this club.
"Whether you get this job six, seven or eight years down the line or now I want to make sure I’m ready for the opportunity.
"I think I am but you're going to be judged by what happens on the football field."