diff --git a/sphinx/ext/imgconverter.py b/sphinx/ext/imgconverter.py
index b95ef2588..95d3fe65a 100644
--- a/sphinx/ext/imgconverter.py
+++ b/sphinx/ext/imgconverter.py
@@ -27,6 +27,7 @@ class ImagemagickConverter(ImageConverter):
         ('image/svg+xml', 'image/png'),
         ('image/gif', 'image/png'),
         ('application/pdf', 'image/png'),
+        ('application/illustrator', 'image/png'),
     ]
 
     def is_available(self) -> bool:
diff --git a/sphinx/transforms/post_transforms/images.py b/sphinx/transforms/post_transforms/images.py
index 6f51bc8e0..758e92f0d 100644
--- a/sphinx/transforms/post_transforms/images.py
+++ b/sphinx/transforms/post_transforms/images.py
@@ -222,7 +222,6 @@ class ImageConverter(BaseImageConverter):
         if '?' in node['candidates']:
             return []
         elif '*' in node['candidates']:
-            from sphinx.util.images import guess_mimetype
             return [guess_mimetype(node['uri'])]
         else:
             return node['candidates'].keys()
diff --git a/sphinx/util/images.py b/sphinx/util/images.py
index 880a0deeb..4746e1c40 100644
--- a/sphinx/util/images.py
+++ b/sphinx/util/images.py
@@ -32,6 +32,7 @@ mime_suffixes = OrderedDict([
     ('.pdf', 'application/pdf'),
     ('.svg', 'image/svg+xml'),
     ('.svgz', 'image/svg+xml'),
+    ('.ai', 'application/illustrator'),
 ])
 
 DataURI = NamedTuple('DataURI', [('mimetype', str),