Monk was named as Michael Laudrup's short-term successor at the Liberty Stadium and slammed the Dutchman as "disrespectful" last March after he expressed an interest in the job.
However, the 35-year-old - now the Swans' permanent manager - says that those claims were fabricated by the agent of Koeman, who has since joined the Saints.
"It did not mean anything to me, it was his agent making all the claims. You just get on with it," he told Sky Sports News. "People choose different ways to do things.
"I met [Koeman] at the managers' meeting before the season and said a quick 'hello' and that was it.
"It is another opponent, we respect him but we will concentrate on Swansea and getting a result."
This afternoon's encounter in South Wales gets underway at 3pm.