You will not get the alliance option in the trade screen until you are very friendly (close) to the race that you are attempting to form an alliance with.
Same thing with Research treaty and Economic treaty's but not to that extent the race in question only has to be somewhat friendly at that.
Even if those options appear it does not gaurantee that the race will agree to ally with you or form such treaty unless they feel it is beneficial for them to do so. You may need to sweeten the pot per say, adding techs, money, ships ect...
I hope that helps.
-Seilore
P.S. I see in the screen shot you provided that you do have a Research Treaty option and you are somewhat friendly with them, if you keep getting closer the alliance option will appear.
