Casting string to generic type that is a string

I'm writing a method to do a intelligent type conversion - using ToString() if the type parameter happens to be a string, otherwise casting but returning null if the cast doesn't work. Basically gets as much information out of v it can without throwing an exception.

I check that T is indeed a string before I attempt the cast, but the compiler is still not a fan:

Cannot convert type 'string' to 'T'

And here's my method:

public T? Convert<T>(object v)
{
    if (typeof(T) == typeof(string)) {
    return (T)v.ToString(); // Cannot convert type 'string' to 'T'  
    } else try {
      return (T)v;
    } catch (InvalidCastException) {
    return null;
    }
}

Also let me know if this is some sort of unforgivable sin. I'm using it to deal with some data structures that could have mixed types.