I want to call a function which will be asynchronous (I will give a callback when this task is done).
I want to do this in single thread.
As others have said, you technically can't in plain C++.
However, you can create a manager that takes your task and does time-slicing or time scheduling; with each function call, the manager uses a timer to measure the amount of time the process took; if the process took less time than scheduled, and it thinks it can finish another call and use up the remaining time without going over, it can call it again; if the function does go over the alloted time, it means the function has less time next update to run. So, this will involve creating a somewhat complex system to handle it for you.
Or, if you have a specific platform in mind, you could use threading, or create another process to handle the work.