There has been speculation on social media from viewers that there may be some tension between the 60-year-old weather presenter and the 47-year-old show host but Kirkwood has dismissed the feud rumours.
Asked in an interview with The Sun if they get on Kirkwood said: "We absolutely do.
"I love Naga and we just have banter. I love the camaraderie between us and everyone. It’s a good, fun job."
Rumours of tension between the two TV presenters has arisen in recent months after several on-air exchanges, including Kirkwood mispronouncing Munchetty's name.
The weather reporter said live on the show back in November 2022: "The winds will be lighter, just a few showers coming in from the north-west and temperatures ranging from nine to 13 degrees, Nana."
Kirkwood quickly added: "Naga, sorry, we’ve got a producer called Nana."
Munchetty responded: "You say that every single time. And I come and visit you and have a cup of tea."
On Christmas Day Munchetty accused Kirkwood of being "stern" with her over the weather report.
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She said: "Carol... I think we're never allowed to ask you about snow on Christmas Day. You always kind of have that really stern look whenever I ask... Doesn't she?"
And when the first coins bearing the face of King Charles III were released in December, Munchetty appeared to make a joke about Kirkwood's age.
The BBC Breakfast host remarked: "There’s the nostalgia. “Carol, do you know that feeling?
“Do you remember you’d get really excited because you’d have a new picture of the Royal Family or a special minted coin. You’d be excited about it and you’d keep it and not spend it.”
Kirkwood replied: “That’s absolutely right and when the new coins came out as well I remember that.
“We lost the thrup’nny bit and we picked up a half pence and a one pence.”