According to the Japanese website Light Novel News, there are 5 light novels that deserve an anime adaptation. The survey was conducted by the editors of LN-News according to the most searched light novels.
Only Sense Online (10 volumes ongoing): MAL; Translation
Chronicle Legion (5 volumes ongoing): MAL; Baka-Tsuki
Set at the end of the 20th Century. Due to the Japanese Empire, an island country in the far east having been conquered Caesar, a resurrected hero from Ancient Rome, it is now being controlled by the neighboring county Eastern Roman Empire! The power that made Caesar the most powerful conquered was called Legion. That is, a mysterious army made up of gathering all the great powers; a giant winged army. The Japanese empire's imperial princess, Fujinomiya Shiori, hides her ambition in becoming the supreme ruler and starts to act. Who she chooses as her trusted commander is, at first glance, a mediocre high school student Tachibana Masatsugu. However, he too is someone who was reincarnated from a past warrior; a resurrected hero whose greatness rivals even Caesar's: Legatus Legionis!!
The Rising of the Shield Hero (15 volumes ongoing): MAL; Baka-Tsuki
Seishun Buta Yarou Series (6 volumes ongoing): MAL; Baka-Tsuki
"Hey, shall we kiss?"
She who was teasing me with these seductive words temporarily disappeared before my eyes.
There could not be a bunny girl inhabiting a library. Azusagawa Sakuta faced a scene that toppled common sense—he encountered a bunny girl, and she is nowhere a normal bunny girl. She is Sakurajima Mai-senpai, a student studying at the same school as Sakuta and a retired yet renowned actress. It was said that starting from a few days ago, those around her could no longer see her anymore, and she came to the library just to confirm this. Is this related to the hit topic on the internet, the unimaginable phenomenon known as "the puberty syndrome"? Sakuta, wanting to know the reasons behind and get closer to Mai, decided to solve the puzzle. However, the situation then developed in an unexpected way—?
In the city surrounded by the skies and the seas, the romance story of I and she began. The brand new romantic comedy presented by the Sakurasou combo.
Tensei Shitara Slime Datta Ken (9 volumes ongoing): MAL; Translation
Sources: Adala-news (fr); LN-News