diff --git a/setup.py b/setup.py
index 7f91d5d2c..56ade5d39 100644
--- a/setup.py
+++ b/setup.py
@@ -29,8 +29,14 @@
 # 'Development Status :: 5 - Production/Stable'
 release_status = "Development Status :: 5 - Production/Stable"
 dependencies = [
-    "google-api-core[grpc] >= 1.26.0, < 3.0.0dev",
-    "google-cloud-core >= 1.4.1, < 3.0dev",
+    # NOTE: Maintainers, please do not require google-api-core>=2.x.x
+    # Until this issue is closed
+    # https://github.com/googleapis/google-cloud-python/issues/10566
+    "google-api-core[grpc] >= 1.26.0, <3.0.0dev",
+    # NOTE: Maintainers, please do not require google-api-core>=2.x.x
+    # Until this issue is closed
+    # https://github.com/googleapis/google-cloud-python/issues/10566
+    "google-cloud-core >= 1.4.1, <3.0.0dev",
     "grpc-google-iam-v1 >= 0.12.3, < 0.13dev",
     "proto-plus >= 1.13.0",
     "libcst >= 0.2.5",