The Peacock Network responded to a gossip item published by website The Daily, which claimed that Gregory was to be sacked due to falling ratings.
Meet The Press has long been the Sunday morning ratings winner, but recently it has struggled to top CBS's news hour Face The Nation.
An unnamed source claimed that NBC has also been unhappy with Gregory's performance since he took over for the late Tim Russert in 2008.
"The rumours recklessly reported by The Daily are categorically untrue," an NBC spokesperson told the New York Daily News.
NBC's representative also insisted that CBS's Face The Nation has been successful largely due to "gimmickry".
There has been a large shake-up within NBC's news division in recent weeks. Ann Curry was sacked as co-anchor of the channel's flagship morning show Today last week, apparently at the behest of her on-air partner Matt Lauer.
Savannah Guthrie, formerly an NBC legal analyst, is to officially replace Curry on Monday (July 9)'s edition of Today.
