The cover of this month's issue of Gangan Joker magazine has announced that the manga series Issuukan Friends. (One Week Friends) will be receiving an anime adaptation. Further details about the project will be announced at a later date.

Synopsis summarized from the manga's official page:
Kaori Fujimiya is always alone because all of her happy memories, including time spent with her friends, disappear every Monday. Deciding that he wants to be friends with her anyway, Yuuki Hase tries to get close to Kaori each week, wishing that she would one day call him "a friend."

Source: Gangan Joker magazine cover

Isshuukan Friends. on MAL


Update January 22
Isshuukan Friends. will be aired in Spring 2014.

PV: http://www.youtube.com/watch?v=TZvQtV2ijHM

Cast
Yuuki Hase: Yoshitaka Yamaya
Kaori Fujimiya: Sora Amamiya

Staff
Director: Tarou Iwasaki
Series Composition: Shoutarou Suga
Character Design: Eri Yamasaki
Art: Satoshi Itou
Art Setting (?): Head Works
Color Design: Ritsuko Utagawa
Filming: Tomoyuki Shiokawa
Editing: Daisuke Imai
Sound Director: Satoshi Motoyama
Music: Irone Toda
Studio: Brains Base
Production: "Isshuukan Friends." Production Committee

Source: Official site

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