The Northern Ireland international is currently in his second spell at Upton Park, but is out of contract at the end of this season.
And with West Ham's campaign ending in less than three weeks, the 32-year-old defender is keen to secure his future at the club.
"Of course I want to stay here," he told The Newham Recorder.
"I am not getting any younger of course, but it would be lovely to be here next season.
"Talks haven't started yet. The manager has already stated he will wait until we are mathematically safe before he starts talking as I think there are a few players out of contract.
"We will wait until that day comes and see what happens."
McCartney has made 23 appearances in all competitions this season.
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