Pietersen hinted that he could retire from international cricket after the series with South Africa due to "obstacles", despite appearing in good form by scoring a century in the drawn second Test at Headingley.
However, Cork insists that the England dressing room are tired of Pietersen's ongoing troubles with the ECB.
Cork told Sky Sports News: "There are obviously players whose patience is wearing thin at the moment; this isn't a one-off story with Kevin Pietersen and I think that when you're in that changing room - and what I'm hearing - is that England players now are actually sick and tired of hearing about Kevin Pietersen in a series that is one of the biggest series England have had since Australia.
"What it does is it takes the focus away from exactly what this is all about. It's not about a Kevin Pietersen story, it's about an England side who are trying to hold on to that number one status."
Former England captain Alec Stewart recently suggested that the current side could handle Pietersen's retirement.