diff --git a/utils/bazel/llvm-project-overlay/llvm/BUILD.bazel b/utils/bazel/llvm-project-overlay/llvm/BUILD.bazel
--- a/utils/bazel/llvm-project-overlay/llvm/BUILD.bazel
+++ b/utils/bazel/llvm-project-overlay/llvm/BUILD.bazel
@@ -2,6 +2,7 @@
 # See https://llvm.org/LICENSE.txt for license information.
 # SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 
+load("@bazel_skylib//lib:selects.bzl", "selects")
 load(":template_rule.bzl", "template_rule")
 load(":tblgen.bzl", "gentbl")
 load(":config.bzl", "llvm_config_defines")
@@ -25,6 +26,24 @@
     "$(STACK_FRAME_UNLIMITED)",
 ]
 
+config_setting(
+    name = "x86_32",
+    constraint_values = ["@platforms//cpu/cpu:x86_32"],
+)
+
+config_setting(
+    name = "x86_64",
+    constraint_values = ["@platforms//cpu/cpu:x86_64"],
+)
+
+selects.config_setting_group(
+    name = "any_x86",
+    match_any = [
+        ":x86_32",
+        ":x86_64",
+    ],
+)
+
 enum_targets_gen(
     name = "targets_def_gen",
     src = "include/llvm/Config/Targets.def.in",
@@ -2326,8 +2345,6 @@
     name = "Exegesis",
     srcs = glob([
         "tools/llvm-exegesis/lib/*.cpp",
-        "tools/llvm-exegesis/lib/X86/*.cpp",
-        "tools/llvm-exegesis/lib/X86/*.h",
 
         # We have to include these headers here as well as in the `hdrs` below
         # to allow the `.cpp` files to use file-relative-inclusion to find
@@ -2335,7 +2352,13 @@
         # `tools/llvm-exegesis/lib` with the `strip_includes_prefix` of this
         # library. This mixture appears to be incompatible with header modules.
         "tools/llvm-exegesis/lib/*.h",
-    ]),
+    ]) + select({
+        ":any_x86": glob([
+            "tools/llvm-exegesis/lib/X86/*.cpp",
+            "tools/llvm-exegesis/lib/X86/*.h",
+        ]),
+        "//conditions:default": [],
+    }),
     hdrs = glob(["tools/llvm-exegesis/lib/*.h"]),
     copts = llvm_copts + ["-DHAVE_LIBPFM=1"],
     defines = ["LLVM_EXEGESIS_INITIALIZE_NATIVE_TARGET=InitializeX86ExegesisTarget"],