Thank you for contacting us.
We do not have an out-of-the-box counterpart of the mentioned control in our suite. However, our controls are built on top of the Telerik Presentation Framework (TPF). This allows you to easily build complex controls from a few simple types of elements.
Please refer to the sample project that demonstrates the idea of how to incorporate a TextBox into RadDropDownList's popup.
I hope this helps.
the Telerik team