diff --git a/doc/whats_new/v1.4.rst b/doc/whats_new/v1.4.rst
index ce16556feb88c..507b22cdf510a 100644
--- a/doc/whats_new/v1.4.rst
+++ b/doc/whats_new/v1.4.rst
@@ -474,6 +474,10 @@ Changelog
   when `radius` is large and `algorithm="brute"` with non-Euclidean metrics.
   :pr:`26828` by :user:`Omar Salman <OmarManzoor>`.
 
+- |Fix| Improve error message for :class:`neighbors.LocalOutlierFactor`
+  when it is invoked with `n_samples = n_neighbors`.
+  :pr:`23317` by :user:`Bharat Raghunathan <Bharat123rox>`.
+
 :mod:`sklearn.preprocessing`
 ............................
 
diff --git a/sklearn/neighbors/_base.py b/sklearn/neighbors/_base.py
index 519db9bead3d3..848c8b7c9dc5a 100644
--- a/sklearn/neighbors/_base.py
+++ b/sklearn/neighbors/_base.py
@@ -813,9 +813,15 @@ class from an array representing our data set and ask who's
 
         n_samples_fit = self.n_samples_fit_
         if n_neighbors > n_samples_fit:
+            if query_is_train:
+                n_neighbors -= 1  # ok to modify inplace because an error is raised
+                inequality_str = "n_neighbors < n_samples_fit"
+            else:
+                inequality_str = "n_neighbors <= n_samples_fit"
             raise ValueError(
-                "Expected n_neighbors <= n_samples, "
-                " but n_samples = %d, n_neighbors = %d" % (n_samples_fit, n_neighbors)
+                f"Expected {inequality_str}, but "
+                f"n_neighbors = {n_neighbors}, n_samples_fit = {n_samples_fit}, "
+                f"n_samples = {X.shape[0]}"  # include n_samples for common tests
             )
 
         n_jobs = effective_n_jobs(self.n_jobs)
diff --git a/sklearn/neighbors/tests/test_lof.py b/sklearn/neighbors/tests/test_lof.py
index 221d78243915f..7233beddafe9c 100644
--- a/sklearn/neighbors/tests/test_lof.py
+++ b/sklearn/neighbors/tests/test_lof.py
@@ -255,6 +255,50 @@ def test_sparse(csr_container):
     lof.fit_predict(X)
 
 
+def test_lof_error_n_neighbors_too_large():
+    """Check that we raise a proper error message when n_neighbors == n_samples.
+
+    Non-regression test for:
+    https://github.com/scikit-learn/scikit-learn/issues/17207
+    """
+    X = np.ones((7, 7))
+
+    msg = (
+        "Expected n_neighbors < n_samples_fit, but n_neighbors = 1, "
+        "n_samples_fit = 1, n_samples = 1"
+    )
+    with pytest.raises(ValueError, match=msg):
+        lof = neighbors.LocalOutlierFactor(n_neighbors=1).fit(X[:1])
+
+    lof = neighbors.LocalOutlierFactor(n_neighbors=2).fit(X[:2])
+    assert lof.n_samples_fit_ == 2
+
+    msg = (
+        "Expected n_neighbors < n_samples_fit, but n_neighbors = 2, "
+        "n_samples_fit = 2, n_samples = 2"
+    )
+    with pytest.raises(ValueError, match=msg):
+        lof.kneighbors(None, n_neighbors=2)
+
+    distances, indices = lof.kneighbors(None, n_neighbors=1)
+    assert distances.shape == (2, 1)
+    assert indices.shape == (2, 1)
+
+    msg = (
+        "Expected n_neighbors <= n_samples_fit, but n_neighbors = 3, "
+        "n_samples_fit = 2, n_samples = 7"
+    )
+    with pytest.raises(ValueError, match=msg):
+        lof.kneighbors(X, n_neighbors=3)
+
+    (
+        distances,
+        indices,
+    ) = lof.kneighbors(X, n_neighbors=2)
+    assert distances.shape == (7, 2)
+    assert indices.shape == (7, 2)
+
+
 @pytest.mark.parametrize("algorithm", ["auto", "ball_tree", "kd_tree", "brute"])
 @pytest.mark.parametrize("novelty", [True, False])
 @pytest.mark.parametrize("contamination", [0.5, "auto"])