diff --git a/pymc/sampling/mcmc.py b/pymc/sampling/mcmc.py
index 4afb93a7fe..1a1fc45e6a 100644
--- a/pymc/sampling/mcmc.py
+++ b/pymc/sampling/mcmc.py
@@ -39,7 +39,8 @@
 import numpy as np
 import pytensor.gradient as tg
 
-from arviz import InferenceData
+from arviz import InferenceData, dict_to_dataset
+from arviz.data.base import make_attrs
 from fastprogress.fastprogress import progress_bar
 from pytensor.graph.basic import Variable
 from typing_extensions import Protocol, TypeAlias
@@ -47,6 +48,11 @@
 import pymc as pm
 
 from pymc.backends import RunType, TraceOrBackend, init_traces
+from pymc.backends.arviz import (
+    coords_and_dims_for_inferencedata,
+    find_constants,
+    find_observations,
+)
 from pymc.backends.base import IBaseTrace, MultiTrace, _choose_chains
 from pymc.blocking import DictToArrayBijection
 from pymc.exceptions import SamplingError
@@ -293,8 +299,8 @@ def _sample_external_nuts(
                 "`idata_kwargs` are currently ignored by the nutpie sampler",
                 UserWarning,
             )
-
         compiled_model = nutpie.compile_pymc_model(model)
+        t_start = time.time()
         idata = nutpie.sample(
             compiled_model,
             draws=draws,
@@ -305,6 +311,37 @@ def _sample_external_nuts(
             progress_bar=progressbar,
             **nuts_sampler_kwargs,
         )
+        t_sample = time.time() - t_start
+        # Temporary work-around. Revert once https://github.com/pymc-devs/nutpie/issues/74 is fixed
+        # gather observed and constant data as nutpie.sample() has no access to the PyMC model
+        coords, dims = coords_and_dims_for_inferencedata(model)
+        constant_data = dict_to_dataset(
+            find_constants(model),
+            library=pm,
+            coords=coords,
+            dims=dims,
+            default_dims=[],
+        )
+        observed_data = dict_to_dataset(
+            find_observations(model),
+            library=pm,
+            coords=coords,
+            dims=dims,
+            default_dims=[],
+        )
+        attrs = make_attrs(
+            {
+                "sampling_time": t_sample,
+            },
+            library=nutpie,
+        )
+        for k, v in attrs.items():
+            idata.posterior.attrs[k] = v
+        idata.add_groups(
+            {"constant_data": constant_data, "observed_data": observed_data},
+            coords=coords,
+            dims=dims,
+        )
         return idata
 
     elif sampler == "numpyro":
diff --git a/tests/sampling/test_mcmc_external.py b/tests/sampling/test_mcmc_external.py
index fc3e6e1551..d7370a560d 100644
--- a/tests/sampling/test_mcmc_external.py
+++ b/tests/sampling/test_mcmc_external.py
@@ -16,7 +16,7 @@
 import numpy.testing as npt
 import pytest
 
-from pymc import Model, Normal, sample
+from pymc import ConstantData, Model, Normal, sample
 
 
 @pytest.mark.parametrize("nuts_sampler", ["pymc", "nutpie", "blackjax", "numpyro"])
@@ -25,7 +25,11 @@ def test_external_nuts_sampler(recwarn, nuts_sampler):
         pytest.importorskip(nuts_sampler)
 
     with Model():
-        Normal("x")
+        x = Normal("x", 100, 5)
+        y = ConstantData("y", [1, 2, 3, 4])
+        ConstantData("z", [100, 190, 310, 405])
+
+        Normal("L", mu=x, sigma=0.1, observed=y)
 
         kwargs = dict(
             nuts_sampler=nuts_sampler,
@@ -55,7 +59,9 @@ def test_external_nuts_sampler(recwarn, nuts_sampler):
             )
         )
     assert warns == expected
-
+    assert "y" in idata1.constant_data
+    assert "z" in idata1.constant_data
+    assert "L" in idata1.observed_data
     assert idata1.posterior.chain.size == 2
     assert idata1.posterior.draw.size == 500
     np.testing.assert_array_equal(idata1.posterior.x, idata2.posterior.x)