This has been a wonderful season to date for the 23-year-old full-back, having played a key role in Saints' astonishing start to the campaign and impressed in his first England run-outs.
Such displays have somewhat inevitably led to speculation Clyne could soon be leaving for pastures new, with Liverpool and Monday's opponents United heavily linked in recent days.
The right-back's deal at St Mary's runs until 2016 and talks are ongoing to extend that, leaving Koeman relaxed about the situation.
"If I have to be worried about those kind of rumours, then I will be worried every day and I don't like that," the Dutchman said with a smile.
"I like my life and I like to be positive. It's no issue."
It is a good job Koeman does not get het up by transfer talk given the summer he had, with Luke Shaw, Adam Lallana and Rickie Lambert amongst those moving on, although that unparalleled talent drain from St Mary's has not led to the meltdown some had predicted.
Saints instead enjoyed their best-ever start to a top-flight campaign and, while things have gone slightly awry of late, they remain in with a serious chance of securing a top-four finish.
Injuries have taken in recent matches and, depending how things pan out in the coming weeks, Koeman may choose to dip into the transfer window in January.
"One is to plan January when you have everybody available then you have to look if you need some players," the Saints boss said.
"If you have a lot of injuries for a long period, that makes it more normal to bring in new players.
"We have to wait because players are coming back and that decision we have to make in two or three weeks."