The US comedy has aired four seasons on NBC, with a fifth currently in the works.
Channel controller Richard Klein appeared to announce the acquisition in a BBC statement, promising "a year of comedy led by... hit US comedy Parks and Recreation".
However, the relevant sentence was later deleted from Klein's section on the BBC media centre website.
The sitcom stars Amy Poehler (Saturday Night Live, Mean Girls) as Leslie Knope, an optimistic, mid-level bureaucrat who works at the Parks department in the fictional town of Pawnee, Indiana.
Rashida Jones, Aziz Ansari, Nick Offerman, Aubrey Plaza, Chris Pratt, Adam Scott and Rob Lowe also appear in the series, which was co-created by Greg Daniels and Michael Schur (NBC's The Office).
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Watch a clip from Parks and Recreation below: