So touching ...

this really romantic.

I've never played Solatorobo...Is there a reason why he cannot love her ? In the game, maybe ?

I was able to play the game via pc emulator. Anyone can play it for free in that way, you can try it as well.
Regarding your question, there's no real implication besides hunches why Gren's feelings aren't responded. All we know is he has a crush on her, officially confirmed in a relationship chart, dubbed as "unrequited love". It can either mean he did confess and got rejected or never told her. It's mostly the latter, judging his reserved and calculative personality.

However it's somehow evident as he's very (if not too much) protective of her in a point insulting her in his presence is enough reason for him to attempt murder.

Why didn't he tell her? Well he's a subordinate and takes her heart above his own, so is possible he's keeping it a secret to not trouble her and also for being aware she doesn't feel the same.