Generic function creates generic object of arguments base

I have the following code:

public class Foo
{
    public void DoSomething()
    {
        DoSomething(this);
    }

    private static void DoSomething<T>(T obj)
    {
        var generic = new Generic<T>();
    }
}

public class Bar : Foo
{
    // properties/methods
}

public class Generic<T>
{
    // properties/methods
}

public class Test
{
    public void TestMethod()
    {
        var bar = new Bar();
        bar.DoSomething(); // instantiates Generic<Foo> instead of Generic<Bar>
    }
}

Is it possible to instantiate a generic class from a derived method with the current type instead of the base type?