I've read various claims of a season 3, however through some digging I've found them to be baseless rumors.
There has not been any hints or annoucement of sorts from any anime studios, nor the original author himself (but hey I don't read Japanese so I might missed out). Those rumors online did not provide sources, only vague description of when and platform.
I understand that many of us yearn for more K-On anime (I myself have rewatched the series many, many times), however please do not be misled by rumors/hearsays.
P.s. - however if you think I'm wrong, please correct me.