UK citizenship for refugee

I have Query regarding my case and whether I can apply for UK citizenship or not.
I am came to the UK Jan 2008 on student visa for 6 month, then I’ve renewed my student visa until I completed my master degree, after that I have applied for post study work visa and been granted the PSW for two years. in 2012 I’ve applied for (out of rules) to renew my visa but whilst I was waiting for the decision I had a dramatic change in my case due to political issues back home which lead me to apply for asylum. The home office withdrawn my out of rules application and granted me refugee leave to remain in Jan 2013 and it’s valid until Jan 2018.
Whilst I was working in the UK full time since 2011. And whilst I have continuously lived in the UK since Feb 2008. I wonder if I can make a case to apply for UK citizenship and passport before the end of my asylum status in 2018 (not to wait toward 2017) but instead apply now.

Any insights in this regards are highly appreciated

I'm afraid it is not possible presently, as far as I can see.
You have to be free from immigration controls before you can apply for Citizenship, i.e. you need to apply for
Indefinite Leave to Remain (ILR) visa first. Good luck.

Student/PSW visa stay is not counted towards settlement so you will have to spend 5 years on refugee status before you can apply for an ILR and then a year later apply for naturalisation/passport