Creating a closure for std::function

I am not sure if I am using the exact terminology , But I'll try to be as descriptive as possible to clear out any confusion .

Suppose I have an std::function variable

std::function<void(int)>  callback ;

Due to some reasons beyond my scope , I cannot change the function prototype. I receive the std::function variable at some point in my code and I have to call it.Something like this :

int a = 10 // just an example value
callback(a); 

Now I have another variable . Let's name it id .

int id = rand(); // Let us assume that rand here generates a random variable
int a = 10 // just an example value
callback(a);

I want id to be accessible inside the callback i.e I am looking for some form of closure . Is there any way to do it without making the id static/global.