No, you can't specifically do that, however you can select a placed drawing on a layout and make it an autotext reference.
Right-click on a placed drawing, choose "Set as Autotext Reference"
Now when you choose the Autotext option in your text block, there are numerous options to place under the "Reference for "[drawing you set]"" section. Refer attached images.
However, could you expand on the reason why you want to do this? There may be another way, depending on your reasons.