The HBO comedy-drama - which follows four young women living in New York City - premiered last night in the US.
"[The network] ordered scripts [for season two], so we are thinking about it," Konner told The Huffington Post. "[It's] really fun and I hope we get to make it."
The writer and producer added that HBO has been giving "smart and creative" notes on Girls.
"We were thinking of the second season almost the next day," she revealed. "It was really liberating and cool. They're the best."
Girls creator Lena Dunham previously dismissed comparisons between the series and HBO's Sex and the City.
"I think once you watch the show [you'll see] that the tone is so vastly different," she said. "That was always my hope - that people watch it and the connections sort of fade away because it's such a clearly different tone."
Girls airs on Sundays on HBO.
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Watch a trailer for HBO's Girls below: