diff --git a/doc/whats_new/upcoming_changes/sklearn.mixture/28559.feature.rst b/doc/whats_new/upcoming_changes/sklearn.mixture/28559.feature.rst
new file mode 100644
index 0000000000000..31da86d63c0f7
--- /dev/null
+++ b/doc/whats_new/upcoming_changes/sklearn.mixture/28559.feature.rst
@@ -0,0 +1,5 @@
+- Added an attribute `lower_bounds_` in the :class:`mixture.BaseMixture`
+  class to save the list of lower bounds for each iteration thereby providing
+  insights into the convergence behavior of mixture models like
+  :class:`mixture.GaussianMixture`.
+  By :user:`Manideep Yenugula <myenugula>`
diff --git a/sklearn/mixture/_base.py b/sklearn/mixture/_base.py
index dd50d39b4fdb0..f66344a284753 100644
--- a/sklearn/mixture/_base.py
+++ b/sklearn/mixture/_base.py
@@ -224,6 +224,7 @@ def fit_predict(self, X, y=None):
         n_init = self.n_init if do_init else 1
 
         max_lower_bound = -np.inf
+        best_lower_bounds = []
         self.converged_ = False
 
         random_state = check_random_state(self.random_state)
@@ -236,6 +237,7 @@ def fit_predict(self, X, y=None):
                 self._initialize_parameters(X, random_state)
 
             lower_bound = -np.inf if do_init else self.lower_bound_
+            current_lower_bounds = []
 
             if self.max_iter == 0:
                 best_params = self._get_parameters()
@@ -248,6 +250,7 @@ def fit_predict(self, X, y=None):
                     log_prob_norm, log_resp = self._e_step(X)
                     self._m_step(X, log_resp)
                     lower_bound = self._compute_lower_bound(log_resp, log_prob_norm)
+                    current_lower_bounds.append(lower_bound)
 
                     change = lower_bound - prev_lower_bound
                     self._print_verbose_msg_iter_end(n_iter, change)
@@ -262,6 +265,7 @@ def fit_predict(self, X, y=None):
                     max_lower_bound = lower_bound
                     best_params = self._get_parameters()
                     best_n_iter = n_iter
+                    best_lower_bounds = current_lower_bounds
                     self.converged_ = converged
 
         # Should only warn about convergence if max_iter > 0, otherwise
@@ -280,6 +284,7 @@ def fit_predict(self, X, y=None):
         self._set_parameters(best_params)
         self.n_iter_ = best_n_iter
         self.lower_bound_ = max_lower_bound
+        self.lower_bounds_ = best_lower_bounds
 
         # Always do a final e-step to guarantee that the labels returned by
         # fit_predict(X) are always consistent with fit(X).predict(X)
diff --git a/sklearn/mixture/_bayesian_mixture.py b/sklearn/mixture/_bayesian_mixture.py
index 7de5cc844b098..466035332eaee 100644
--- a/sklearn/mixture/_bayesian_mixture.py
+++ b/sklearn/mixture/_bayesian_mixture.py
@@ -254,6 +254,10 @@ class BayesianGaussianMixture(BaseMixture):
         Lower bound value on the model evidence (of the training data) of the
         best fit of inference.
 
+    lower_bounds_ : array-like of shape (`n_iter_`,)
+        The list of lower bound values on the model evidence from each iteration
+        of the best fit of inference.
+
     weight_concentration_prior_ : tuple or float
         The dirichlet concentration of each component on the weight
         distribution (Dirichlet). The type depends on
diff --git a/sklearn/mixture/_gaussian_mixture.py b/sklearn/mixture/_gaussian_mixture.py
index 74d39a327eb7c..2796d0fc3bacc 100644
--- a/sklearn/mixture/_gaussian_mixture.py
+++ b/sklearn/mixture/_gaussian_mixture.py
@@ -669,6 +669,10 @@ class GaussianMixture(BaseMixture):
         Lower bound value on the log-likelihood (of the training data with
         respect to the model) of the best fit of EM.
 
+    lower_bounds_ : array-like of shape (`n_iter_`,)
+        The list of lower bound values on the log-likelihood from each
+        iteration of the best fit of EM.
+
     n_features_in_ : int
         Number of features seen during :term:`fit`.
 
diff --git a/sklearn/mixture/tests/test_gaussian_mixture.py b/sklearn/mixture/tests/test_gaussian_mixture.py
index b9ee4e01b0120..488a2ab147e83 100644
--- a/sklearn/mixture/tests/test_gaussian_mixture.py
+++ b/sklearn/mixture/tests/test_gaussian_mixture.py
@@ -1236,6 +1236,7 @@ def test_gaussian_mixture_setting_best_params():
         "precisions_cholesky_",
         "n_iter_",
         "lower_bound_",
+        "lower_bounds_",
     ]:
         assert hasattr(gmm, attr)