Operator as and generic classes

I want to make a method:

object Execute()
{
    return type.InvokeMember(..);
}

to accept a generic parameter:

T Execute<T>()
{
    return Execute() as T;

    /* doesn't work:
    The type parameter 'T' cannot be used with the 'as' operator because
    it does not have a class type constraint nor a 'class' constraint */

    // also neither typeof(T), nor T.GetType() are possible

    return (T) Execute(); // ok
}

But I think operator as will be very useful: if result type isn't T method will return null, instead of an exception! Is it possible to do?