Kadokawa Shoten Animation answered to J-Cast News's interview that the TV anime of "The Melancholy of Haruhi Suzumiya
" to be aired in April is the re-airing of the first season.
The cover note of Newtype magazine March issue says "Suzumiya Haruhi Anime restarts in full throttle. The TV anime will be aired from April".
Source: J-Cast News
Edited on Feb 6th============
Newtype magazine March issue doesn't have any new information of the second season.
Sources: Scan of Newtype
& Scan of Newtype (zoomed)