I need to inject EF context per request. Is there any way to implement it?
What do you mean by injecting? Do you mean to apply dependency inversion principle on it? If yes then do you ever envisage yourself swapping out your EF context with some other context which adheres to same contract?
To me you should encapsulate EF context somewhere in framework, so that every request gets EF DataContext. Apply DI on your repository. Later on your repositories might have different kind of contexts and you can switch repositories with each other.