diff --git a/Lib/ctypes/util.py b/Lib/ctypes/util.py
index 0c2510e1619c8e..c550883e7c7d4b 100644
--- a/Lib/ctypes/util.py
+++ b/Lib/ctypes/util.py
@@ -96,8 +96,11 @@ def find_library(name):
     def _is_elf(filename):
         "Return True if the given file is an ELF file"
         elf_header = b'\x7fELF'
-        with open(filename, 'br') as thefile:
-            return thefile.read(4) == elf_header
+        try:
+            with open(filename, 'br') as thefile:
+                return thefile.read(4) == elf_header
+        except FileNotFoundError:
+            return False
 
     def _findLib_gcc(name):
         # Run GCC's linker with the -t (aka --trace) option and examine the
diff --git a/Lib/test/test_ctypes/test_find.py b/Lib/test/test_ctypes/test_find.py
index 66ff23e72b5e10..7732ff37308848 100644
--- a/Lib/test/test_ctypes/test_find.py
+++ b/Lib/test/test_ctypes/test_find.py
@@ -125,6 +125,9 @@ def test_find_library_with_ld(self):
              unittest.mock.patch("ctypes.util._findLib_gcc", lambda *args: None):
             self.assertNotEqual(find_library('c'), None)
 
+    def test_gh114257(self):
+        self.assertIsNone(find_library("libc"))
+
 
 if __name__ == "__main__":
     unittest.main()
diff --git a/Misc/NEWS.d/next/Library/2024-01-21-16-32-55.gh-issue-114257.bCFld5.rst b/Misc/NEWS.d/next/Library/2024-01-21-16-32-55.gh-issue-114257.bCFld5.rst
new file mode 100644
index 00000000000000..6f02ff9e62617d
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2024-01-21-16-32-55.gh-issue-114257.bCFld5.rst
@@ -0,0 +1,2 @@
+Dismiss the :exc:`FileNotFound` error in :func:`ctypes.util.find_library` and
+just return ``None`` on Linux.